As far as I know, congress shoes, as I've heard these called for men, were perfectly accurate.
{See below} The elastic itself may not be perfectly accurate--too stretchy, wrong weave, I dunno--but that's going to be almost impossible to upgrade, and what's most apt to be wrong will be things that would be found in
any <$200 shoe. What looks odd to me are the leather (is that suede?) the shape of the sole (too wide at the arch), the kind of sole (that's not rubber instead of leather, is it?), the visible stitching on the top of the sole around the edges. I mean, the shoe is clearly wrong, but not because it's a congress gaiter.
Let me see if I can find an example of a period one. Well, here's never the way to judge what's accurate, but NJ Sekela is selling them and he's known for his accuracy. But you want to look at originals.
http://www.njsekela.com/product_info.php?cPath=46&products_id=744
It looks like there's some talk about congress gaiters in this forum, especially if you do an edit-find to see what's on the very long page:
http://www.thehcc.org/forum/viewtopic.php?f=23&t=1054&start=25
Just don't see more info quickly, and I'm not sure how much it's worth it. I've seen them in political cartoons too, because stuff political types tended to wear them.
Note that the term "gaiter" has nothing to do with the gaiters that look like spats that reenactors use to cover up inaccurate shoes. I didn't know they were still doing that, honestly. But anyway, I agree that those shoes that you bought are inaccurate at a glance, but not because they have elastic on the side.
Oh, wait, you're female. --slaps forehead-- I didn't realize because congress gaiters were worn by both men and women. When I needed to dress up fancy, I'd sometimes borrow my wife's. Fugawee sells cheap but sorta authentic congress gaiters for women, or used to. Yeah, here,
http://fugawee.com/civil war shoes.htm , about $129, plus shipping probably.
I have no idea if women wore gaiters, I mean the spats-type gaiters, not the shoes they called gaiters. Certainly they'd be smaller and more delicate than the big old things that soldiers wore.