Yeah, no that's not going to make any difference. The flapper seems to be working fine, and it looks like the Toto flapper. The problem isn't in the tank. And you can't get just any Korky 3" flapper. There's a specific one that's right for the GMAX flush on that Carrollton -- Korky 2021BP, available online and at most hardware and home stores. Just Google it. As Jim says, that flapper is exactly the same as the Toto THU331S (like it's made on the same mold by Korky and put into a different package). But like I say, the flapper looks like it's working fine.
I would be concerned that that aftermarket 400A fill valve would not be giving you enough refill water in the bowl, but the water spot in your Carrollton seems to be where it is supposed to be at the beginning of the flush, so it ain't the fill valve either.
The big, big (and completely-obvious) issue is that you're not getting any push from the siphon jet at the bottom of the bowl. That initiates the siphon with a burst of water across the bottom of the bowl and into the trapway. What's happening in your toilet is that the siphon isn't beginning until the bowl fills with all of the flush water, then the siphon takes hold and pulls everything from the bowl. Because you have no siphon jet.
There's a bunch of rust or something in front of the jet. Put on some rubber gloves and stick your finger in that hole and see if there isn't some kind of obstruction there. It may be that hard water has caused crusties or something to block it. It's frankly kind of weird. (I did have this problem in a 40-year-old American Standard toilet, and I got it working acceptably just by poking around with my gloved finger and dislodging a bunch of junk inside the siphon jet hole.) It's also possible that at some point somebody disconnected the tank from the bowl and in reconnecting it some foreign object caused a clog at the tank/bowl connection that causes all the flush water to go through the rim holes instead of through the siphon jet, but that's less-likely.
One other option is to pour a bunch of CLR down through the overflow riser in the tank and let it sit for a number of hours before trying to flush again. The goal is to clear out the path through the porcelain that delivers water to the siphon jet.
Here's a cutaway of virtually-every gravity toilet (although it doesn't show the siphon jet), so that you can see what's going on. Once water fills the trapway, a siphon causes all the contents of the bowl to be evacuated and go out the bottom, after which the siphon breaks and you hear that gurgle from air being sucked into the trapway. The siphon jet fills the trapway quickly. Otherwise, the water level in the bowl has to rise until it fills the trapway, then the siphon slowly evacuates the bowl.
That your bowl ultimately evacuates completely after the siphon finally begins suggests that there is no obstruction in the drain line. This is a failure to fire by the siphon jet, pure and simple.
