First of all, how did you arrive at the number of 35,000? A 12 word seed phrase missing 2 words gives 2048*2048 = 4,194,304 possible combinations. Even excluding the 15/16 of those which would produce an invalid checksum, you end up with 262,144 possibilities.
I would also use btcrecover to do this. Since you do not know an address, then you would instead use an address database: https://btcrecover.readthedocs.io/en/latest/Creating_and_Using_AddressDB/
Set it up with your database, tell if the 10 words you do know and the locations of the two you don't know, and let it run. It will try every possible valid combination and check if the first x number of addresses in whichever derivation path(s) you specify have ever been used.