Haven't handled a Pika II, but I'd pick the RAT-1 out of the three you mentioned. The Pika II design just didn't resonate with me. Having used both a RAT-1 and Tenacious, I prefer the RAT-1 by a big margin. It just handled better and felt more solid in hand and during use.
If you don't mind blems, you can pick up a Blur from
kershawguy for under $50. For just a tad over, you can even get one in S30V. The Blur is comparable in size to the RAT-1 and Tenacious. For a slimmer knife more like the Pika II, also check out the Leek, Skyline, and OD-1. A composite blade Leek would be my top pick from those (can also get a blem of that within your budget).
If you like the Spyderco designs, keep an eye out on the exchange here for a Delica4, Endura4, or Centofante3. Retail for those seldom drop below $50, but occasionally LNIB ones will show up on the secondary market for under $50. I think I've seen a Stretch go for under $50 before as well.
Large Buck Vantage might be another worth looking at. The Select and Avid models fall within your budget. The Pro model sometimes gets there as well, and they too pop up on the secondary market for under $50 sometimes.