I'm not an uberexpert, but the systems you mention don't really interact normally, so I'm inclined to believe this is either a problem with your console (loose screw, loose connector on the back of it, etc.).

Additionally, maybe a ground somewhere is dirty or loose, or some corroded wires are touching and causing power from the headlights to affect the speedo?

If I was you I would start at the dash console. Pull it out a bit and take a look at the back. Check all the screws to make sure they are clean and tight, and press on all the plastic male multiwire connectors to make sure they are snugly fitted to teh back of the console.

If this doesn't solve the problem trace the wiring throughout your brick to make sure you don't have corrosion. Remember, the early volvos have defective wiring that corrodes horribly due to heat and age, so it is worth the time to go over all exposed wiring in the car, especially in the engien compartment. Get a small wire brush, some wire cutters, and a roll of electrical tape. Clean off any wiring that appears to be corroding with your hand, brush it clean, and reseal it with the tape. Also, cut into the larger black harness sheathing about 2" to check for hidden corrosion... 2" is about the farthest up the sheathing corrosion reaches. If its bad cut into teh sheathing until you hit good wire and fix it to that point.

Most of teh wiring for the rear electrical system run up the left side of teh car, so check this thoroughly if all else fails. Remove the paneling on teh bottom all teh way up the left side and check for corrosion, bad grounds, etc.

In the end I believe cleaning and repairing all the wiring, tightening up the connections, and cleaning/reseating all your grounds will solve this problem.

Regards,
Rick