Like bblr said, if it needs refinishing, spend that money to get one that's in better shape or buy it for a beater with no intention of worrying about how it looks.
My vote would be to skip it - - there's just too many good looking used classic P's out there due to all the LEO 40 dumping. Some of these guns have led a tough life, but more are is great shape, mostly carried and with relatively few rounds.
Redoing anodize, as others of said, will absolutely positively change frame dimensions. Think about it. The original frame is bare alloy, it goes into an acid bath with a positive charge, which causes the surface of the metal to corrode under controlled conditions to grow a layer of aluminum oxide. This layer will reduce the diameter of holes, so they will have been machined slightly oversize to account for the reduction in ID.
When you strip the anodize, usually in a caustic bath, the size of that hole grows as the aluminum oxide material is removed. The hole is larger than it was when first manufactured. Now the nhe new anodize will grow within the hole and bring the size back towards original size, but that material is gone so it can't be brought back to original spec. Holes will all be oversize and frame dimensions will change - - this is why SIG won't strip and re-anodize.
