Overseeding fairly new Centipeded lawn

I would wait until May or June.

Wait a little longer
It's probably going to be fine
I found and read this today you may appreciate LINK

From that article:
How to Seed and Overseed Centipedegrass
If you need to plant new centipedegrass, you can use seeds or sod. Keep in mind that centipedegrass is slow to establish, taking about 28 days to germinate. It can take up to three years for a centipedegrass lawn to become uniform and dense. Plant seeds in late spring and early summer for the best results.

Does your existing centipedegrass lawn look a little patchy? Overseeding may be the solution. Spread seeds over your lawn after aeration for the best results.

Some homeowners overseed their warm-season lawns with cool-season grass for winter color. However, centipedegrass doesn’t handle this well, and it could cause damage to your existing lawn.

Centipede grass struggles in shade, especially under large oaks. I guess it might have a little better shade tolerance than, say, the notoriously bad shade tolerant Bermuda grass, but “better than bad is still bad”. Are you getting at least 4 hours of sun daily? If so, you might have better results with St. Augustine grass, solid sodded. There’s no St Aug seed. There’s a reason that neighborhood yards with older, more established landscapes in the south have mostly St. Augustine grass.