They might not allow it (no chance of marketplace sales or follow-on volume), but if I were better off I'd drop the $10k or so and do something random just for the experience. Maybe a bunch of different little designs on one IC.
https://efabless.com/open_shuttle_program/2
There are 40 slots, so you might not get selected. But the open shuttle uses the same software and framework as chip ignite.
The idea is simple... a grid of 4x4 LUTs, each geographic neighbor has 1 bit in, and 1 bit out, there are 16 states, each with 4 outputs.
Turns out that this route-less FPGA can do some fairly amazing things, at least in theory. Now I intend to find out.
The really old blog I had about it - https://bitgrid.blogspot.com/
In fact, our project for the previous Google shuttle was an FPGA-like device which also routes data using logic cells. Here is an introduction to the idea:
https://github.com/fiberhood/MorphleLogic/blob/main/README_M...
It worked in simulation and the chip is currently scheduled to be shipped to us on September 6. There were 2 or 3 projects that were more conventional FPGAs.
An academic project that takes yet another approach to this design space is: