Does a vow conditioned on the supplicant not having to make up for the days of Ramadan that he fasted count as a vow of stubbornness (nadhir al-lajaj), necessitating expiation if he were to make them up again due to doubt?

You do not have to re-fast the days whose fasting you doubted was invalid, because doubt concerning an act of worship after completing it does not affect its validity. Do not give in to these whisperings (waswas).

As for your vow not to repeat the missed fasts (qada'), if you do re-fast, you must offer an expiation for breaking an oath (kaffarat yameen), unless the vow or the breaking of it was under the influence of whisperings, in which case nothing is required of you.

As for the days you did not make up (qada') at all, you must make them up. If you are unsure of their number, then make up what will give you certainty or a strong presumption that your obligation has been fulfilled.