wow - very good. i need to digest all this and get back to you regarding if your level works and what the total is, but i think it works.
for now, in the original level, the block gets shot under your tank at the end, so it is the top anti-tank that fires the last shot. 3^23 shots later, the other anti-tank's shot makes it to the end, and then the anti-tanks alternate every 3^23 shots. the last multiplier (coefficient) "A" in the equation (A*3^23) is indeed very important, so the total is now very much greater! i'll do a calculation later, but off hand it looks to me like the total is now on the order of about >16*11*3^23 or >16 trillion. i'll have to try your multiplier with my 3^24 counter and see what happens... of less significance, all of the previous lower order parts can be further multiplied by adding bricks and regressing mirrors and such just to squeeze every little extra available move out of the thing.
the only other compact counters i've come across are simply multiples
of 3 (ie base 9, base 27 etc). in other words, base 9 looks exactly the
same thing as trinary. the binary stuff really didn't go anywhere useful.
i'll have to play around with the tunnels to see what happens. i was already
using them in a slightly more compact (and faster) clock drive in the 3^24
counter, but i didn't know they could be used as they were in your level.
-steve