Caps could work. I think I'd want to try and track down what's causing the issue first, as the headlights might be the first symptom of something bigger. (For example I had three friends with early 2000 Dodge trucks with electrical gremlins. Turned out that among other things what the bad electrical thin was doing was leaking current into the coolant, and electrolysis was eating the aluminum engine parts pretty quickly.)
The wiring described should give a pretty decent ground, assuming that the car body is free of electrical resistance. That is where are the bulbs grounded, and how does that go back to the spot where you put the big wire. Between unibody construction, weld through primer and spot welds, and glue/sealant between parts there's no guarantee that the body itself isn't the issue. But I haven't really looked an a Subaru's wiring in 25 years, so I could be way off. I'm just spitballing.
The obvious choice for quick and easy fix, if there are no other symptoms in the car, is to put LED replacement bulbs in it. The drivers ought to handle any voltage spikes, and the some of the new Halogen replacements actually work pretty well with stock reflectors.