Getting a Poland permanent residence permit on the basis of forever waiting for a temporary residence permit?

I have lived in Poland for 3.5 years already and am on my 3rd attempt at getting a temporary residence permit. Each time I apply the foreigners' office takes almost an entire year to issue a decision, eventually coming up with some excuse as to why they cannot grant the permit. And each time they deny the application I submit a new application and get a new stamp in my passport from them, thereby extending my legal stay in Poland (although I could also just rely on the US-PL bilateral agreement).

My question is, if this cycle continued for another 6.5 years, would I then be eligible for a permanent residence permit, even though I never would have had a temporary permit? The conditions for granting the permanent permit simply say I must have legally resided in Poland for ten years.

No. You might be able to apply for a "tolerated stay" permit in those circumstances, but in your case, it would almost certainly be denied.

The law regarding permanent residency says that you have to have been temporarily resident - but because you never obtained a temporary residence permit, you haven't started the clock.