Spindle palms can eventually exceed 15 feet tall, but they take a while to reach that height. They are great palms. Mine is about 6 feet tall (not including the pot that its in, including the pot its a bit over 9 feet). I have seen some for sale locally here that exceed 10 feet tall and Im sure you can get them even larger in areas where they actually grow year round! So eventually you can expect it to reach 20 feet tall, but its a medium sized palm so it will never reach towering heights, or at least not until they are several decades old!
Generally when Im in Florida I see specimens around 10 feet tall, but there are deginitely taller.

You can try bottle palms. Spindle palms can survive brief freezes and are just really robust palms in general, bottle palms are much more cold sensitive but do great in warm climates like Florida if temperatures dont go below freezing. But they have a much cooler looking trunk (hence the name bottle) and they will stay shorter if height is a concern. I've seen some sold here that are about 8 feet in height (not including the pot) but they dont get too much taller than that. I have seen them in Hawaii at about 10- 15 feet tall but thats a good 30 years of growing if you plant them young. And personally I think they look the best when young.

Good luck!
-Alex

Thanks, Alex, the reason for the height concern is that I want to put them in a couple of patio planters next to our hot tub and the screen there is 17 feet.

I appreciate the input!

I have seen several spindles who's leaves topped out over 20' tall, but it took them a while to get there. Most looks sort of 'spindly' by that point, but I recall one in Thailand that looked like it would keep growing.

If you are planting your Hyophorbe verschaffeltii in a pot, it is very unlikely it will ever make it to 20' (unless you plant in a really large pot). But your climate could support a palm of 20' in the ground in exceptional soil (S Florida soils are not usually that good). Here in California it would take a spindle palm a good 20 years to even make it to 15'... they are simply too slow and a bit marginal in most areas here. I have seem some approaching 10' but those are exceptional palms.

Here are some tall spindle photos:
Hawaii

Here is one in Thailand at 20+ feet tall and very robust (lots of clay in Thai soils)

and here is a good 20' palm in Taiwan (good soil there, too)

Here is about the tallest one I have seen in California (over 20 years old)... leaves top out around 15', maybe a bit less.

Wow, okay.

I think we're going with bananas. I like the bottle palms, but the swollen bottom are over-sized for the planter. My husband wants some nice tropical leaves.