I thought the bridge had to be a bit closer (in other words, no third pickup would exist)?
that has to do with scale length and bridge choice... rather than number of pickups. although 3 pickups on an LP is tight. but if it fits between the current two pickups its fine. if the bridge studs end up close too the bridge pickup cavity then you need to worry - but thats what rulers are for
one thing. refretting a guitar is all well and good. but re fretting a refretted guitar is something else. the slots do wear out so there are more issues to think of with a re-refret than there are a refret.
also, bobs suggestion of redoing the binding is good - because refrets with binding are the hardest type and you probably dont want to do that just yet. well actually gibson refrets where you have to keep the binding nubs are the hardest type. so yeah, if you redo the binding your options are more and cost is less (allowing for the extra cost of tools involved for doing a gibson style refret)