All season tires

Can I put T rated tires instead of H rated ones on my GTP?

I tend to use Michelin HydroEdge or Goodyear Assurance TripleTred, but they are only T rated.

I cannot find good ones with H rated.

yes, you can put them on there, but you'll maybe notice a less stiff sidewall, and you won't want to exceed the speed rating of them.