When thermo initially calls for heat, furnace will come on normally. After a decent run of maybe 5 minutes max, it'll shut off, and then the inducer motor will click on and off. After a longer run, the inducer will click on initially for maybe only a second, and it gradually begins to stay on a little longer each time it clicks on, until finally the furnace will usually complete another longer (~5 min run), and then process starts all over again. Any ideas?

I had a tech in and we checked the following to no avail: pressure switch (replaced both, no change), condensate pump seems fine and no change even if I manually drain the catch, inducer motor sounds fine. I also installed two new mother boards; one off brand, which caused the fan to run with no heat; and one OEM which had no effect to the cycling behavior. So I'm doubting its a relay on the board, though the clicking does sort of sound like a relay clicking, and it'll click during a longer run randomly as well.

I am wondering why the inducer gradually runs for longer. Maybe a partially blocked vent pipe could cause a slow buildup and a slow release of gases, which could cause the pressure switch to interrupt the cycle until gasses are sufficiently vented after a longer run?