I would not remove the peat "crap" as you say. Peat is a valuable planting medium that retains moisture. It's very good to use in potted containers. Use what you have...amend with the soil medium you mentioned. Especially if going to leave it in a container. You need all the peat moss you can.

Most hibiscus grow to be a small bush/large plant. IMO it will only grow as large as the container provided. That said. I'd repot it in as big as a container as you can. And NOT root prune it at all.

Do a little research/homework online on Peat Moss, Container Growing and Root Pruning.

Enjoy your new beauty.

The dampness could be because it was recently watered at the nursery.

It currently looks very healthy, but it does look like there are at least 2 plants in there. If you are going to repot it, you could consider to divide it out.

Without knowing the condition of the rootball, I would sometimes root prune and sometimes not, before putting it in the new pot or same pot after pruning.

For almost any transplant, you can expect leaf drops but kudos if there aren't any.