If one were to connect an air pump and air stone INTO the 2L pop bottle so
that the yeast mixture was constantly bubbling: The net effect would be
that your output from the bottle would be CO2 enriched air which
continuously bubbled into the aquariium (or reactor). BUT, the yeast
reaction would never turn anaerobic, which means the product would simply be
CO2 and water. The yeast would never die, and the kit would never have to
be restarted or replaced. Theoretically you could just add another cup of
sugar each week to keep up the CO2 production.

Does this seem feasible? I'm thinking that the yeast population might grow
too big and therefore need "trimming" once in a while. I'm thinking of
using some sort of split aquaclear filter which would have a hinged lid on
one side (to open to add sugar), and a bleed screw on the other side to
bleed off excess water and yeast. The top would obviously have to be
sealed.

Yes, this may sound eccentric, but in theory it should work.

Incidentally:

(aerobic) Glucose + Yeast --CO2 + Water + energy

(anaerobic) Glucose + Yeast -- CO2 + Alcohol + energy

If it does, I claim patent before Nutrafin can grab it.