I would go for Stormy Mondays that have been slightly overwound to be hotter. The key to the tone on the first album really is the 59 Les Paul itself, the long neck tenon, fat neck, pots and caps all have a part to play. The good news is that Lovepedal have made the COT 50 to recreate the tone, especially if set to just breaking up. It's the best "plexi" voiced pedal I've ever tried and I urge you to give it a go. You'll also need a tube amp with a rich clean tone if you don't already have one.
The tone on Brown Sugar is my benchmark for a perfect guitar sound and I've been trying to recreate it for years. If you ever get enough money together a 59 Les Paul re-issue will get you close but not all the way there. Pearly Gates really is a unique guitar. Good luck!