The most reasonable board for hobby PCIe (< $100) right now is probably the SQRL Acorn, it was designed for mining but it turned out to be pretty useless for that purpose. There are cheaper FPGAs with PCIe support coming onto the market, but they tend to be low on fabric since they are designed for low end applications (Lattice Crosslink NX).

I think there are a few fundamental problems with FPGA compute offload. First is that, as niche products, FPGAs are always a node or two behind the leading edge, so their logic gates run slower than CPUs and GPUs; even their "hard" compute blocks are not as fast. Second, the fundamental nature of FPGAs as a "sea of logic" mean that routing delays reduce your max frequency, or make pipelining necessary thereby incurring latency. Third is memory; historically, FPGAs have not supported high-bandwidth GDDRx, and if you're crunching on something you generally want bandwidth. The latest high-end FPGAs do have HBM but they are quite expensive.

So why would anyone want something that's slower and more expensive? Well, you have to be doing something special, like a lot of custom parallel processing pipelines, or with hard realtime requirements. Basically, a niche, and that doesn't lend itself to economies of scale.