With the dragonfruit, you may simply want to leave the plant behind and take a good number of cuttings with you. It will have to pretty much grow all over again, but at least you will be taking a lower risk of failure.

With pineapple, and the other plants, you might consider making new plants (via cuttings and whanot), that way you could transport them easier.

How much time do you have before you go to Iceland? You said that the plants could be in a soil-less mix. Does Iceland's customs specify what they mean by soil-less? Would a peat/perlite mix be considered soil-less according to their requirements? If so, you could probably start repotting all of your plants into a soil-less potting mix now. If they have enough time they will be able to establish into the new mix before shipping and will suffer a lot less stress. Shipping will cost most but I think the chances of your plants living far outweigh the costs of shipping. Especially considering the possible difficulty of reacquiring these plants in Iceland.

If repotting in a peat/perlite soil-less mix is not feasible it is possible to bare root the plants. I have done it a few times and most trees survive if given the proper care. I've had trees go bare-root for up to 5 days. If you search some the forum there are some posts about the care of bare rooted trees from Thailand. I think OhioJay gave excellent guidelines for the care of the a bare rooted tree. I've included one of the posts in a link below.

Of the trees you have listed, the easier ones to bare root and ship would probably be: mango, pineapple, banana, barbados cherry, vanilla, miracle fruit, dragon fruit, and bacupari. I am not sure on the others because I do not have experience bare rooting them. Maybe others on the forum would. I would expect those plants with finer root systems to be much harder to bare root. I could see passionfruit and jaboticaba being difficult.

Your plants for bare rooting and shipping sound like the will work. I've tried both wet newspaper and sphagnum moss. I didn't notice much of a difference between them but I would probably recommend the sphagnum over newspaper because it can get into all the little spaces of the rootball easier than a newspaper.

The aftercare is going be very important. Make sure the plants are potted up immediately (if barerooted) into a high humidity environment. Some people put bags over each individual plants, others mist, and some into a greenhouse. I think OhioJay puts them into bags in his greenhouse. Not entirely sure though. Good luck.

Here is a link that might be useful: Bare root after care

There is also no promise that they will be allowed in if they find any pests, mold, etc. on the tree. It may simply end up in the giant sink dispoal.

I still need to investigate what defines "soilless" a bit better, but bare-root would be easiest to take with and I know that'd qualify, so that would be preferable. Unless the survival rate is notably different, of course. But we only have limited spaces in our suitcases, and obviously taking something along in a suitcase is both the fastest and cheapest method.

Before I can bring them overseas, I have to get a phytosanitary certificate. So if anything doesn't pass, I'll know before I try to take it, and can give it to someone else locally rather than just have it get thrown away.

Thank you very much for all the tips! :) Especially knowing that bareroot for a few days is okay; that'd give me time to take care of getting the stuff to repot after I get there without having to have everything prepped before I arrive.

I'll check out those aforementioned links. :)