Sorry, I should have been more specific. This is for the DMP-BDT220 Blu-Ray player. It seems like there should be a way to sync the Panasonic remote with my TV, but if not I'll just working with separate remotes (or a universal, like your suggested).
They removed that ability in 2012, probably to cut costs. So what you're asking is impossible. If you really like the Panasonic remote, get a 2011 or earlier model from Panasonic parts site. It will work a sony tv, among others. IMO your money is better spent on a universal. They start around $15.