I think the tricky part for you is that you work with hardware, that might make it difficult for people to understand you working from home, but given that all your work isn't in the lab or at a test bench, you might be able to negotiate a few days at home to work on the other stuff you do (documentation, analysis, whatever it is).
There is always the nuclear option: Say you are quitting and see what they will offer you. Of course, you have to be willing to lose your job if they call your bluff.
I recently went through this as I had a new position I was accepting. When I gave my manager notice, I didn't mention accepting a new position, but casually mentioned I was going to look for something with more flexibility. Our conversation then went along the lines of "What can we do to make you stay, how much flexibility do you need?". I have no doubt I could have walked out of there with more money and several days a week of either adjusted schedule or working from home. Though I think once you say you are quitting, you should just quit, not accept their counter.
This is coming from a position where it was made clear before the culture was not to allow working at home, but during the conversation my manager offered having me report to someone else so I could have the flexibility I wanted. Sometimes, just the threat of you leaving is enough for you to get everything you want ...