Okay, first things first. The Korky 528 will fit your K4590 Portrait toilet. If you need to replace the valve, the Korky will be easier to install.
Now to the Wellworth 4520. As Jim discussed, the most likely place that the water is exiting the tank is through the flush valve. The fill valve can't be the culprit because you had the water turned off at the wall, so even if for some reason there was a siphon through that valve, the valve at the wall was closed. So somehow it's going through the hole that has the flush valve in it. Either through (1) a crack in the flush valve, (2) a siphon down the overflow riser through the refill tube (which only happens if the refill tube isn't mounted above the top of the overflow riser on the little clip; if it's sticking down the overflow riser, that's a likely problem, if it's "daylighted" above the overflow riser, it isn't your problem, or (3) right through the mouth of the flush valve even though you just replaced the flapper.
So let's go through it:
(1) We're sure we have the right flapper for this flush valve, right? If the flush valve has never been changed, it takes that flapper that looks like a flush ball, or an avocado. Presumably what you put on looks just like what you took off, right? HD didn't sell you the wrong flapper, I hope.
(2) So...a question. When you turn off the water to the toilet and it ends up empty in the morning, does "empty" mean that there is absolutely no water in it? Or does empty mean that there's a little water in the bottom, maybe right to the bottom of the mouth of the flush valve that is covered by the flapper? If so, than the likely culprit is the seal between the flapper and the flush valve, one way or another. If the tank is totally, completely empty, then there is either a crack in the bottom of the flush valve or there is a leak around the gasket under the flush valve. But you can't lose a whole tank around that gasket and not have it end up on the floor, so I'm thinking crack. If "empty" means that it goes down to somewhere above the flapper, then it's either a siphon (see above), or there's a crack at or around that spot on the flush valve.
So...to solve: (A) if we're thinking that it's going out between the flapper and the flush valve, first, check the chain length. Do you have at least one ring of slack in the chain when the flush arm is at rest, slack that you can see. You don't need much, but sometimes if the chain is totally-taught, it can hold the flapper imperceptibly-open. Sometimes the flush handle rotates a little and that leaves the flush arm, when it is at rest, a little higher than you originally set it, so it's worth a double-check. Also make sure that for some reason when you put the lid back on it doesn't affect this, like pushing down on the handle. Also make sure you don't have too much slack in the chain so that it's getting caught under the flapper when it closes, or otherwise the flapper isn't getting hung up. (B) If not A, then run your finger around the mouth of the flush valve. Is it completely-smooth? Is there any gunk on it that might hold the flapper off in one spot? You can Brillo it a bit and see if that doesn't make a difference. Also, there are kits that you can get that put a new gasket around the mouth of the flush valve, but we can get to that later if we have to. (C) If not A or B, then maybe there is a crack. Run you hands all over the flush valve and make sure no cracks.
Is there no little disturbance of the water in the bowl at all after the toilet has sit for a few minutes? Any ripples on the surface? You might see just a little bit. To confirm that the water is going from the tank into the bowl, you can drop a little food coloring in the tank. Start by trying to get it just down at the bottom, and see if you can see it being sucked into or around the mouth of the flush valve. If there's no colored water in the bowl after a while, then you can agitate the water just a smidge so that now the tank is filled with dyed water. If the dyed water then starts leaking into the bowl, there's a crack in the overflow riser somewhere above the flapper, most likely.
I could tell you just to go get the Korky Complete toilet overhaul kit, which comes with a 528 fill valve and a new flush valve and flapper. It's probably an hour-long project, which involves removing the tank from the bowl. It's fun, and Korky's instructions are excellent, but unless you are super-enthusiastic pulling off the tank and then reseating it can seem like a lot of work. However, Korky has phone people who can walk you through it if you have any difficulties, or you can ask questions here. Before we get there, let's go through these simple steps first, as outline above.
Let us know what you find.
Good luck!!
PS If you want to post a low-res photo on here of what's in your tank, give us an establishing shot of the whole tank with the top off, maybe one with the water at the level that it drains to, and a closeup of the flush valve. Maybe we can see something.