Oh, and the third prospect for evolution of a recurrent nova system : the donor star gets a sudden dose of stellar hiccoughs - say, it swallows a gas giant, and does a sudden big release of gas, which piles up fast enough on the recipient to make it go Boom. Essentially, at random.
But it's unlikely that a donor star would be precisely stable in it's mass loss rate - it is drinking at the Last Hydrogen Saloon, has already left the Main Sequence, and is evolving rapidly (in stellar terms) ; so what it throws off onto the recipient is likely to be changing, even if (by human terms) slowly changing.
When the recipient star (the originally more massive of the pair, now the smaller in mass, and a white dwarf) goes through it's red giant phase, that is likely to shed some mass onto the star which would become the donor, changing it's evolutionary path. How long would it take for the donor star to settle down after that episode of late middle-age spread?
A 4th option - which I don't recall having seen discussed because it violates Occam's razor : if you have your recurrent nova pair orbiting away, occasionally having a little-bang, but they are actually in a wide triple - that's not an inherently implausible stellar system. Hell, our neighbours (Alpha Centaurus A and B, plus Proxima Centaurus) are just such a triple. And if A and B were merrily cycling away, doing their recurrent nova thing with no obvious trend towards SN-Ia fireworks. Until star C (Proxima - alike) comes barrelling back in for it's quarter-million year fly by. Now, that could certainly stir things up - particularly if it were a close pass.
And a wide triple like that wouldn't leave that much of a mark in the subsequent supernova remnant, would it? Not like the multiple star shenanigans going on in Eta Carinae/ the Homunculus nebula.