How about elephant ears? The original tuber can be expensive but can be brought inside for the winter and replanted in the spring the next year.
Ferns? Giant philodendren? Orchids--some big box stores carry some inexpensive orchids and they have a long bloom period.

I would think a palm could do well outside for the summer. Be sure to be careful to expose it to the sun in increments to prevent burning the leaves. I take all my houseplants outside for the summer.

A banana like 'Siam Ruby', burgundy leaves with chartreuse splashes. But any banana will do.

Any castor bean "tree" which can get to be 9 feet or more in one season. I like 'Zanzibar' and 'Carmencita Red'.

Any Brugmansia with its big, perfumed trumpet flowers.

A tropical-looking vine like Mina lobata, passion flower, or Thunbergia. Some Clematis look tropical, too.

Some daylilies look very tropical, for instance 'Mauna Loa'.

Papyrus is my favorite!

So, it's perfectly possible to have the tropics in Minnesota: these plants love our summers and many can be brought inside for the winter.

Brugmansia- Datura- Malibar Spinach- Lilies in pots, or in the ground, Torenia, Thumbergia, Impatiens balfouriii, Hibiscus Moeschuto, hardy Hibiscus, Mina Lobata, Mirabilis, New Zealand Purple ricinus, are a few from my yard I usually do not go without-

Many of your suggestions I am familiar with, but will have to look up quite a few, too. Sounds like fun. I am thinking I will have to figure out a way to build some sort of wall or trellis where I can hang many of these plants to give it that thick and wild feeling. I wonder if I can get DH to build me a little tiki bar? Now, if I could convince the crows and seagulls to dress up like parrots and cockatoos. . .

Thanks!

If you go for New Guinea Impatiens, try to go for the taller growing varieties. They will probably be the older releases. They are much more vigorous, usually have better leaf variegation, and will give a better tropical effect. And fertilize and water the bejeebers out of 'em.

If you decide on Orchids make sure they are shaded, they do not like to be in direct sun.

I lived in the tropics and grew my orchids in pots hanging from a mango tree.

I do have a thriving cactus garden in Minneapolis that all stays outside year round if you want to try for the desert look.

Canna lilies might be another choice, the flowers are showy and the foliage comes in various colors, including stripes. GaryStPaul