Monty- you're correct on scoring/burning, but I know of no way to avoid that.
Your pesky little nuts are nylock or similar, and they are not accessible on the inside of the frame. Your nuts live between the black metal back plate 7 the outside of the frame, and if you can figure out how to get them off you have my admiration & respect. There is about 0.4" clearance behind the wiring-panel/plate, and I can barely touch one w/my pinky iirc but cannot get any tool on them. I unscrewed the OEM phillips head screws insofar as I could till the nuts wouldn't yield any more; that gave me a tiny gap behind the screw heads. Then I muscled, pried, tweaked, fudged, angled, fangled, mangled, strangled, swangled & swore the original solenoid out. Then I slipped the lower edge of the new solenoid's bracket into the gap behind OEM phillips screw heads for a resting spot, drilled two undersized holes above the OEM screws and within the bracket bolt slots, & installed tapping screws so any idiot (ne) could R&R the thing.
Here is another idea. Solenoid bracket holds solenoid w/single small bolt & nylock. Once the small bolt is removed you can tap (plastic hammer or mallet) the solenoid out of the bracket (down only), then tap the new one up & re-install the bolt. You might want to get a way longer replacement bolt, add a short piece of tiny pipe as a shim on both head & nut side (so you see & can get at them easily next time).
Here's another idea- drill out the phillips screws & punch them back into & hopefully out of the back of the plate.
Here's another idea- get a mudflap (~$20 or less at a truck supply joint near you) & trim it to lay on the batteries. It can ride there and won't offend hardly anybody. I just did that on mine:
Wish I'da thought of that a long time ago, like when I bought the mudflaps. Now I can lay on the flap and work on that stupid backboard w/impunity.