Those engines are INSANELY expensive. NASA has been using stirlings for various things for a very long time. They do have engines that have ridiculous life ratings, but they require watchmaker-like manufacturing, assembly and fitting with current designs.

If you can find good ways around having the valve in the hot space (if using a piston) brayton is actually quite a nice cycle to work with.

Like a jet engine/gas turbine=Brayton Cycle.

Braytons have been made with turbines as well as with pistons. Turbines are far more common today.

As others have said, the cost/weight penalty to recover exhaust heat compared to what you would get makes it impractical for automotive applications.

Looking as a similar waste problem, steam locomotives are nearly all open cycle, discharging the expanded steam to the atmosphere rather than condensing it and feeding it back into the boiler.  This might seem incredibly wasteful given that water supply was often one of the biggest headaches associated with operating these locomotives.  As it turns out, some railroads with a lot of desert miles tried condensers and found them to be more trouble than they were worth.

6-stroke engine adds a water injection and steam expansion cycle between the exhaust and intake stroke.

Not surprising to hear they are expensive, I mean this is a nuclear reactor we are talking about.

I expect that whenever we get serious about offworld colonization we will probably use bigger reactors with more conventional cooling loop systems. These little things might provide enough power for a probe or a scientific outpost with no more than a few people. But we are going to need things that can drive large scale industrial processes for life in space to become anything more than a prestige project of large nation states.

As for the 6 stroke engine idea. I have liked the sound of that since I first heard of it. But I would guess there's some issues there that prevent the tech from filtering down to commercial automobiles. I can see how spraying water on a hot piston head could cause trouble.

Aside from perhaps obviating a pneumatic starter on the APU, those batteries don't have anything to do with MEA.  I can't think of a current aircraft that isn't employing a ckpt batt or main batt.

Electrically driven ECS, smaller federated HYD loops, stuff like that - more efficient than conventional engine air bleed, traditional hydraulic loops, etc.  The 787 batteries are nothing like that.

http://www.lb.boeing.com/commercial/aeromagazine/articles/qtr_4_07/article_02_1.html

Yeah, scaling is difficult for conventional stirlings. They get heavy very quickly. Standard alternator designs are a delicate impedance match to make sure the engine doesn't run away. And from an efficiency standpoint, it's tough to get the heat to go into the working space of the engine instead of anywhere else.