Is there an underpaid fringe 1C available? I'd trade Nemec for one of those, and add if they also take Palat.
No.
You don't "shop" Nemec -- the kid has legit NHL 1RD upside. And no one "shops" underpaid top 6 centers for the same reason. They're too valuable.
The best center available in a trade now is likely Mika Zibanejad. And as much as I like Zibanejad as a player, I don't think that, watching him this year, this is a player you'd want to pay $8.5 million for the next three seasons after this one.
At the deadline, you might see a couple of better 3C options come on the market, like Gourde or Dickinson. But they're not available now.
The two centers I'd like to take a swing at both play in California. Getting Marco Sturm from San Jose would be a cheap and relatively low-cost depth move and we could fit him in under the cap. Sure he's not a difference maker, but he's a guy who could hold down a 4C role competently in the NHL.
The guy I'd really like is Alex Turcotte from Los Angeles. He's not only a good friend of Jack Hughes, but he's also a very adequate defender with tremendous speed whom I still feel has some untapped offensive upside. While there would certainly be some cost involved here, it might prove a savvy deal down the line. Not sure if it's possible to provide him from a very competitive LA team but it's certainly worth the phone call. The Kings are thin on the blueline and the Devils could afford to dangle an NHL-ready guy like Misyul or Hatakka plus a prospect or two outside of the star-level top guys like Nemec or Casey.