So here's what I would do if I were in this situation. I wouldn't build a graphics processing unit per se, but instead would build a highly parallel SIMD CPU organized in workgroups, and with workgroup-local shared memory. These cores could be relatively simple in some respects (they wouldn't need complex out-of-order superscalar pipelines or sophisticated branch prediction), but should have good simultaneous multithreading to hide latency effectively.

Then, if you wanted to run a traditional rasterization pipeline, you'd do it basically in software, using approaches similar to cudaraster (which is BSD licensed!). The paper on that suggests that it would be on the order 2X slower than optimized GPU hardware for triangle-centric workloads, but that might be worth it. The good news is this story gets better the more the workload diverges from what traditional GPUs are tuned for - in particular, the more sophisticated the shaders get, the more performance depends on the ability to just evaluate the shader code efficiently.

It would of course be very difficult to make a chip that is competitive with modern GPUs (the engineering involved is impressive by any standards), but I think a lot would be gained from such an effort.

I should probably disclaim that this is definitely not legal advice. Anyone who wants to actually play in the GPU space should plan on spending some quality time with a team of topnotch lawyers.