That's an excellent point wwtknoyb

Basically, in order to pull off check-in at BUD, you may well need to present proof of an onward flight from TAO to a different country departing before 2p the day after arrival in NGB (this stop triggers the 24 hour clock).

Then, you could try the original strategy with border control in NGB.

That's a lot of moving parts, and not for the feint of heart or the feeble, but maybe it would work.

Still, I'd like to retract my earlier tacit seal of approval.

ETA: Maybe you could ask FM for a true stopover in NGB? Then, you could ostensibly pick up the second segment at a later date.