Cool... I'm an 80's guy at heart, too. It seems like you're right where you need to be with most of your rig. Just a little fine tuning ought to get you the rest of the way there. Based on your comments, I think I'd start by trying some EL34s. They're a little softer than KT77s and have bigger mids, slightly more rounded highs, and a little less low-end. A lot of those 80s tones were EL34s and although the KT77s are pretty close, they are a little different. I think rolling a few tubes through the pre might help, too. I'd try either a Sovtek 12AX7LPS or a JJ ECC803 in the PI slot. For the rest of the positions, you might want to try either the regular Mullard Reissue 12AX7 or their CV4004, possibly some Ruby 12AX7 AC5 HG+ (which may be what's in it now, or at least a variation of the Chinese 12AX7B). I know Peter uses the CV4004 in some amps, too, and I've had good luck with all of these tubes in various amps. If you can get your hands on some NOS glass, it would definitely not be wasted in the Paul!
FWIW, I'm slightly jealous of your Paul. It's one of those amps that I'd love to at least play, someday. Every clip I've heard, it just sounds so sweet. Definitely one great amp! I've been playing a Herbert for the past year+, and I just put in an order for a VH4... that'll be here Wednesday. Diezels are addicting!!