Blake - I think I have an idea of what you like. If you are like me, then you like lots of long, snaky, windy ball paths, with a long entrance and long return travel. There are games with ramps that tend to be very straight, like Stern Star Trek (which I own and love, but not for its ramp action) or Johnny Mnemonic which, to me, do not win awards for best ramps. Also, loops don't count.
Unfortunately, the machine that best fits this description is White Water, which is easily a $4k machine in some parts. You may have to bend the rules of what constitutes a ramp to get the budget under $2k.
Judge Dredd, for example, really only has 3 "official" ramps, one of which is very hard to hit and has such a short entrey that it is hard to call it a ramp. However, the pop-up hole at the upper right corner of the playfield acts very quickly and puts the ball onto a wire-form back to the left inlane. It pops up quicly enough that it feels almost like a ramp. This machine might be called "3.5" ramps.
No Fear also only has 3 "official" ramps, although one of the ramps splits off into two possible paths. This might be another "3.5" ramps game.
Here's something interesting about both Judge Dredd and No Fear. Neither have pop bumpers! It seems that, in many cases, if you want more ramps, you start running out of space for other things, like pop bumpers. Even Demolition Man only has space for 2 pop bumpers. You may want to think about if this sort of compromise is something you would accept.
Or you just spring for an "A" game which manages to squeeze everything in.