I would use a steamer not an iron.

I don't have a steamer. A damp press cloth?

I did test the ink, definitely not water soluble. But melting, I don't know.

I took a silk screening class in 1977-78 at Fort Mason when I lived in San Francisco. I always used a cotton press cloth for ironing what I printed, but it was never damp.

What kind of felt are you talking about? The fiber content is important.

For the cotton weave, you can use a damp press cloth, but I would use a dry one for the felt, especially if it is wool. However, you can use "surge of steam" on wool felt, if you have that setting on your iron.

I would iron it from the back.

If you iron it from the back, you need to put a press cloth under it, as the ink can get transferred to the ironing board.