The TreK will do just fine with such tyres. I'm not a fan of Bridgestone tyres, but the Contis are fine, perhaps not quite as grippy as the Dunlops, but you can choose Pirellis, Michelins or Metzelers and have several miles of fun riding.
In case you want something very similar to the Dunlops, you might want to try either Pirelli Corsa3 or Michelin Pilot Power ones, which are nice road tyres. Or, should you want more mileage for your long trips, try Pirelli Stradas or Conti Road Attacks, or Metzeler Z6's.
After all, the bike is just an ordinary but a tall-ish sport bike, and runs well with a number of different sport or sport-touring tyres, depending on your riding habits.
Fitted Avon Storm ST . High speed stability significantly improved, ride quality smoother with less bump thump and traction better. No improvement in feedback compared with Dunlop but yet to experiance heavy rain ( honest! )