I know a windscreen makes a difference for the Esbit. If I can squeeze it in with all my other unfinished projects I will attempt to build something like what you described. Sure, it complicates a simple idea but it sounds like fun. Any excuse to play with fire is OK (smile).

The problem I foresee is getting enough air into the system. Alcohol vaporizes to provide the pressure. Only vapors burn so there must be some vaporization with the Esbit. However it doesn't vaporize as readily as alcohol or liquid fuels so pressure may be difficult to achieve without forcing air into it. Maybe study how solid fuel rocket engines work for an idea?

I might be missing something in my logic.