This is a great question. I personally have not built a rocket stove, but I have built a small TLUD kiln to make char. The mini TLUD was based on an old 1 gallon paint can, the leftover can from a can of beans and two soup cans. I tried this just to experiment. Sure enough, it worked. I had to tinker with it a little bit but I eventually got it to produce wood gas that burned completely and totally without any smoke at all. And in the end I got a little black beans can worth of charcoal.
So given the my little experiment worked, I bet you could get a RMH in a compact package. One issue worth noting though—my little TLUD took about 90 minutes from start to finish. Possibly this is not enough time to fully heat your mass or cook what you want to cook. But I think it is a great idea and I say go for it!
I have only made 6” versions but I have read about a 3” one and several 4” systems however it seems pretty well documented that 6” or lager is the way to go as smaller systems are fickle and difficult to operate.
I've seen more and more rocket stoves, especially mexican ones, fed by fans through small holes in the sides of the burn chamber. Also, I've seen small can gasifiers, with a computer fan fed into the bottom, and slits cut in the top and holes at the bottom.
I believe Erica got a 3" one to work, but wasn't happy with the results.
Batchbox rockets can be shorter than originally thought and still operate well.
The riser can be roughly 3 timed system diameter with no real issues.
That makes for an 8" batch box with a 24" tall riser, as measured from the base of the box, so fitting it under an oven should be a non-issue.
Flip and John Anderson have done some of the earliest work on rocket ovens and even kilns, and their rockets are all basic cob cooking rocket.