"The power company and a few different electricians tell us nothing is wrong with our wiring, power, or the washer itself. "

If that statement is 100% accurate you have a bunch of hacks for electricians. If I had assurance I would be paid $2k plus air fair,meals and other expenses AND every single one of those electricians would get on their knees to eat a dog turd,I would come find the problem (find it but not necessarily repair) on condition if I failed no one owed me a dime. Any competent electrician should make you the same deal. BTW you can save the cost of air fare if this house is located in NC Tx. What else can I say other than tell electricians you don't put up with dawdling service

I would check all of the torqued connections in the panel, including the ground connections, and make sure that all of the landing points on the ground bar and neutral bar that are meant for just one wire have just one wire.

If by "(in various rooms)" you mean the same rooms all the time and never in the other rooms I would suspect one of the hot legs.

Call your utility company they may have a lose connection on the neutral wire. They also will inspect your main meter for you .