For the temperatures you are quoting I can only think of Java Moss as being suitable. It can grow in water and out of water on damp wood or soil. Be sure to soak your piece of wood in distilled water for as long as possible, start today, until you get ready to tie some moss to it.

Here is a link that might be useful: Java Moss

Oh, I didn't know java moss could be grown out of water. Can any other aquatic mosses be grown this way? Maybe fissidens, xmas moss, or flame moss?

Any suggestions for ferns or fungi?

The only one I can think of that's small enough is Java Fern - Microsorum. It will extend its fronds out of the water if the humidity is high enough. It's a tropical species and will probably require an aquarium heater and a fairly low light intensity to thrive...which of course may then limit all your other planting choices.

I believe that all the mosses that are being sold as aquatic mosses are actually mosses that occur naturally in very wet places or near bodies of water. The only moss that I would tend to call entirely aquatic is Fontinalis but even that may be found emersed.
Your best bet is to try the one you like best and see how it performs.
Not really into ferns and fungi.