Not sure what you mean by skips. If the wheel is centered between the brakes/seatstays and also between the chainstays near the bottom bracket and is pulled back as far as it goes into the dropout and the QR is tight enough, it should be good. Does it "skip" while riding on the road or while shifting it on a workstand? Is it not going into the gear, shifting itself out of the gear, or the chain skipping over the cog?
Congrats on the leverless tire change.
Oil is good, grease is better.
2007 Peter Mooney w/S&S couplers/Terry Butterfly
1993 Bridgestone MB-3/Avocet O2 Air 40W
1980 Columbus Frame with 1970 Campy parts
1954 Raleigh 3-speed/Brooks B72