This is from an Australian perspective, so I have absolutely no idea if these games were released in the US.
I can't think of any AVP "trigger by $xx" games but there was Jewel of Arabia on the Spectrum/I-Game platform (1 cent game, $50-$100 jackpot). There was also Apache Spirit on the BlueChip (AU1) platform - again in Australia, no idea if it was anywhere else.
Most/all of the AVPs (aka BlueChip Neo) I've seen have the more common style of random jackpot where once the smaller jackpot hits its ceiling the contribution is diverted to the next smallest progressive until the "stuck" jackpot is finally triggered (which isn't guaranteed of course, the game could randomly trigger twelve minors and two majors while the mini is stuck at its limit for four months as it's all up to the RNG). Naturally, if a jackpot is won before its ceiling it resets to its base amount.
And yes, other manufacturers - probably the most memorable to me aside from Jewel of Arabia would be the Konami Wild Fire jackpots from the Endeavour/K2V era.