Slime sucks. Use RideOn instead. Go ahead and put it in the tires. Inspect regularly for stuff stuck in tires. On the other hand, the smallest and cheapest Slime air compressor is an awesome little tool for the price, size, and weight. Make sure the engine is running and held at a fast idle when operating--wouldn't hurt to pull the headlight plug to redirect current capacity (won't make any difference on an '86).
RideOn can be cleaned off with plain water and a tube patched. Not so with Slime. I keep a new tube in the tow vehicle and patches in the tool kit. On unsupported rides far from home I do make room for a spare tube.
I've replaced Tdub's rear tube and/or tire several times with only the tools in my customized tool kit, so, yes, a TW rear tire and tube can be dismounted and remounted anywhere. Your dealer's service department is pulling your gullible leg.
Plan on 4-6 small CO2 cartridges to air up the rear tire sufficient for highway use. Easier on the battery than the Slime compressor. I carry both.