Is there a Vario page album that's like a hardcover book?

It is possible a vintage springback style album may do the job for you. I guess they are still available as new as well. The key is to find one the right size for the Vario sheets. 

I wonder if the Vario pages would actually stay in the binder. Paper has some texture, but Vario are slippery. Have you experimented with compression binders and plastic?

I concur with what philatelia pointed out. I wonder if the Vario pages might slip out, either if the album was dropped, or simply slowly slipping/tilting over time due to gravity and the heaviness of each page.

I have a number of sizes of springback binders from different manufacturers. I will test them with Vario pages when I get home. For sure, the smaller "letter-size" binders that are more suitable for the Vario pages won't hold a lot -- ~25 pages? If you have a lot of Vario pages, expect to take up a lot of shelf space.

Also, unlike ring/post binders, there will be a minimum number of pages you must have in the springback binder -- it needs enough to clamp tightly.

I have always used ring binders -- takes up minimal space to maximize number of Vario pages.

angore makes an excellent point that I didn't even consider last night when I first posted. Basically, Vario pages will not work well for display purposes using either spring-back or post binders, unless they are displayed at angle like the dealer display racks shown above -- they are heavy.

To use spring-back or post binders, album page manufacturers sell their own stockpages that either:
1) are on paper, or
2) are hard stockpages that have a fabric/soft extension on one side that allows it to be flexible and all the pages to "bend" near the binding.
They aren't cheap.

The only other cases I've seen where people used Varios in non-ring binder albums, they were inserted in page protectors to provide flexibility near the binding. That will allow you to use post binders, but the page protectors are almost certainly too slippery for the springback binders.

Given that, I elected not to go test my springback binders to see if simple Vario pages would stay in position.

Best wishes on finding a solution... keep us updated!

Thanks for all of the replies people! I didn't even know about a binding called "springback," thank you very much for this. Just to "get my foot in the door," I think i will get a few vario pages and place my stamps in there, just to see what I actually have, how much space they take up, and help to plan how I might like to ultimately display them.

In the end, i would like to custom print some white pages with things like the Stamp artist biography, inspiration etc, and then use clear mounts for the stamps, and then put it all in a post binder. But for now, Vario it is.