This does a good job of capturing the first part of the problem. Note that Xilinx did make an "open" FPGA part, the 3000 series, it did not do well for them.
The critical thing to understand, is that FPGA users (the big ones, not the casual ones) don't want them to be open. They want the information they program into them to be secret so that their hardware is not easily duplicated by the folks in China and mass produced to under cut them. You can't patent schematics. So these folks want to have a way that a board can be assembled in China but not reproduced there in a way that isn't an exact clone (which you can get blocked as a counterfeit product).
Ok, so where does that leave us? Well it might be easier to create your own FPGA design, have TSMC make it on their cheapest process. And then try to sell those chips.
And if you're saying "Jeebus Chuck! That isn't 'easy' at all." you would be right. And that is why a 200Mhz general purpose CPU is easier to turn into a "custom chip" than an actual custom chip.
So where does that leave us? Well, all the bits between HDL and chip can be done, in a low scale way, either in simulation or on bulk small scale hardware. You can program CPLDs to be simple Logic Units (LU) for your FPGA and wire them together on a PC board. You can find the things that need to be parameterized (intra-LU timing, global clocks, I/O configuration) and build tools which can synthesize, place & route, and download to your "pseudo" FPGA. And if you have all that tooling, and you can show it works, you might be able to get a partner to make some small scale parts for you (200 - 1000 LUs)
It won't happen over night, that is a 5 year plan minimum I think. And you have to get over the hump of developing tooling for an FPGA that may never exist. On the plus side it should be good for several Masters level projects and probably a PhD or two, and if your simulation work was robust you might become the 'standard model' for testing assumptions about reducibility of different constructs into hardware[1]
[1] Sort of the Lena[2] for FPGAs.
[2] A playmate digitized by USC which became the standard image processing image for research.