I totally understand the perspective of saving parts to save money as I've been there before - on a budget. However looking back I really don't think there's much value in doing so depending on how you approach your electronics. For me, I'm looking to use the electronics as a tool to complete a project, I'm not looking for a project to fit the electronics so the chances of undertaking a project that happens to be able to utilise an FPGA I found is extremely rare. Quite often recovered electronics do not work 100% which only leads to frustration, wasted time and money. Personally, I suggest to just spend $30 on an FPGA. It's going to be a tiny fraction of your total build cost and will potentially save a lot of time and heart ache. It's also the best way to practice electronic design.
Edit: Also, why bother spending loads of time attempting to re-ball FPGAs? It has next to zero value for general knowledge or skills in a career. Spend your $30 on an FPGA and use those 10 hours you've saved learning how to make badass FPGA designs! Top FPGA designers can charge lots of $!