Okay, so now I think I've got the heat point across, lets concentrate on the other part, cooling.
First, 1kg to 2.2lbs to 998 grams is a silly conversion

1kg is by definition 1000g.
Second, the other important factor is COOLING the engine from that heat.
We have to also think about how many MJs of heat we can pull out of the engine block during these various conditions.
There are various cooling factors in place. From inside the cylinder, and in particular this car, we have several cooling areas:
- Coolant: Cools the walls, heads, and exhaust headifold.
- Oil: Cools the walls, valvetrain, and pistons (there's also piston oil squirters in this engine supposedly)
- Fuel: In our engine, cools cylinder wall, piston, and exhaust valves.
- Air: This does lots of duties actually

It keeps the radiator cool so it comes back to temp, it keeps our charge temps cool so the air in the cylinder is cooler, and it helps cool the oil when flowing over different components. Its component cooling is minor, but the radiator one is HUGE.
At a lower RPM, both Coolant and Oil flows slower, which lessens their cooling values. As RPM raises, Oil moves quicker, Coolant moves quicker, and fuel is injected more often. All of these raise our cooling capacity.
When we run lean, we take out a very important one: Fuel. The unburnt fuel (hydrocarbons) have a HUGE heat capacity.
Your equations for BTUs released doesn't take in to account that when running at WOT nice and rich, not all of it burns. And the stuff that doesn't burn can soak up A LOT of that heat that was released.
Even with that though. WOT at steady state cannot almost never be done on even a load bearing dyno. The engine still gets too hot and the dyno fans cant push air over the radiator fast enough. WOT on an engine dyno like an OEM does has special cooling setups. Intake Air is chilled, the coolant usually goes through essentially a big air conditioner, and still some engines can run too hot for WOT steady state.
So lets play with your numbers here (not going to vouch for their validity, but they'll be close enough

)
Idle = 8BTUs
Cruise = 50BTUs
WOT = 280 BTUs - Unburned adjustment: (11.9 = 0.8 lambda. Theoretically speaking we'll graciously burn 90% of it, which is probably an over-exageration) and get 250BTUs.
Now, we need to look at cooling contribution:
Idle cools pretty well assuming your coolant fan and water pump are working, but on the other hand,Sports bikes for example, have idle overheating issues. They get WAY too hot at idle, despite the minor BTUs. The main reason is just getting airflow over the radiator. We're operating at stoich with just enough torque to overcome losses, so all component temperatures usually remain fine. At stoich, fuel only contributes minor cooling, as most of it burns.
WOT. We're generating the hypothetical 250BTU. Our RPMs steadily rise, increasing coolant and oil flow, keeping our valvetrain and cylinder walls mostly in check. The oil squirters help keep the bottom of the piston cool. We run RICH, which helps our power improve, but probably even more importantly, it absorbs a ton of heat. The piston's crown and exhaust valves stay cool. We probably have a cooling capacity while moving through the air of 230ish BTUs, leaving only 20BTUs into the engine. But even at a track, we don't run WOT continually, and as soon as we lift off, we have more cooling capacity than generation, especially with RPMs staying high, so around the track we can hopefully stay cool enough to keep going for the day. But maybe we don't. Some people on this forum have had some overheating issues where the engine starts to cut boost because of temperature limits. (There's also one thing we're leaving out, but running too rich can start to raise exhaust gas temperatures and manifolds will start to glow, as combustion starts to happen slightly in the exhaust and all the heat the fuel absorbed gets transferred into the exhaust.)
Lean Cruising, we have airflow and plenty of coolant circulation. Oil circulation is also fine. But we're missing one important thing. Fuel cooling. It all burns away (at least until we start misfiring), leaving very little fuel behind. Remember heat and temperature are two different things. We might have less heat, but where it goes and gets absorbed raises the temperatures. The piston crown gets hot. The spark plug gets hot. The exhaust valve gets hot. We might only have our theoretical 50BTU going through, and our coolant stays nice and cool, but parts not touched by coolant, that are cooled and protected by fuel, are no longer protected.
That's where the issue arises.
Also just as a point of contention:
Lets flow 20lbs/min of air (about mid RPM), but run at that 1.1 lambda and 0.8 lambda:
1.1 lambda: 9.35049206 g / s = 416BTU
0.8 lambda: 12.8569266 g / s = 572BTU (lets do the 90% thing again here) = 514BTU
Rich is making more heat (MOAR POWAH!), but the cooling caused by fuel negates a lot of it, and we don't blow up.
Lean is making less heat, but will easily put a hole in your piston.
Of course using your 50% vs 100% we'll quickly see lean takes in more heat overall, but it would while cruising as well.
While your argument about total heat works in general, it's missing the time aspect.
I can boil water on medium heat or high heat. High heat takes less time, but both eventually raise the temperature.
In this case our medium "lean" heat will last much longer (the whole time your cruising!) then the high "rich" heat (WOT), and that time could eventually do damage.
That should make it clear that while rich may make more heat, lean's heat is more dangerous, because the heat it makes is absorbed into components you don't want.
Also remember heat transfer takes time, we might have less heat to transfer, but you spend more time cruising than you do going WOT, and you have less cooling capacity on components in the cylinder.
Every production lean burn engine I know of to date does something to address these issues. (And has fancy catalysts for the NOx, which we're ignoring as you don't have a catalyst anyhow

)
First, all of the lean burn engines built to date have used a high compression ratio (at least for their time period), increasing the efficiency of the combustion process (converting more the energy acrobatically into pressure, and not waste heat).
Chrysler had a trick timing system (one of the first mass production electronic spark control systems by the way), which worked quite well for the time. It modified timing to increase efficiency. It had careful temperature monitoring that would disable the system and retard timing to lower temperatures. (Though we don't want to retard too much, as suddenly a lot of the heat will be wasted and cause the same issue!). It wouldn't pass modern emissions (NOx wasn't a deal at the time), and it suffered reliability issues mostly related to the computer.
Cummins achieves their system for gasoline by using a double injection system. A very lean initial setup (Like 28:1) is placed in, and then a rich mixture is put in quickly (about 7-9:1). The rich mixture ignites quickly, and expands out, which both helps prevent misfire, and raises the flame speed (and thus the time it takes to burn), which increases the engine efficiency, keeping waste heat down. Regardless, Cummins engines are heavy-duty, and have extensive cooling to deal with the extra waste heat.
Honda does a similar process, but via different means. By using stratified injection, where the AFR next to the spark plug is rich, but the overall mixture is lean (basically its non-uniform, but the average is lean), so we save fuel, but we can start the combustion as it's rich there, and the initial flame propagation is like-wise fast, helping prevent waste heat.
The Focus has none of those things. It has no way of keeping waste heat down by having a stratified injection, it's not a high compression engine. It's just not made for it, so you'll suffer the normal consequences of excess heat and wear for no reason.
I'm not saying you in particular will blow up, but keep this in mind moving forward. Lean cruise adds heat to important combustion components far more than the standard stoich would. More heat is more wear on the components even if you don't push them far enough to wreck your combustion chamber.
Is it worth the 2-3mpg?