If you put the cold into the bottom and the hot into the top (with the plumbing aimed horizontally to avoid vertical stirring) the degree of mixing is minimal. Without heat below / cold above to drive convection it takes literally decades for water to mix a vertical inch by diffusion.
Yup. My pond (which I've been mentally comparing this against) holds about 18k gallons by mid-summer and that's pretty obvious if you dip a foot in. The top 6" is nice and warm but below that it's shrink-your-twig'n'berries cold. Even after the kids go swimming(=mixing) there's not a noticeable change in temp...I think I was splitting hairs.
One thing that could be tough is aiming the pipes horizontally. Most of the tankers I've seen have the port in the bottom (the center of a wall if it's vertical). Most normal people wouldn't want to try punching holes in the tanker so they'd have to route the pipes in through the existing port and around the inside of the tank....the hot pipe will be in contact with some cooler water and some convection will occur.
Mixing doesn't matter if you can heat the whole tank though and at this size it may not matter anyway. When you get right down to it, that's a lot of water.
Heat travels faster by conduction. But you're still talking months, not minutes, to make a dent on temperature equalization. You're interested in hours, and you're just fine at that timescale.
Why hours? I thought the idea was to build up the (majority of the) heat over the summer for use in the winter, which means you're storing it for months. If that's not the case then why is there so much water in the system? Maybe there's a misunderstanding on my part.
Which is a fantastic insulator as well as a helpful storage medium. Your main concerns are vertical conduction by the tank wall and heat transfer to/from ground water if you have significant underground flow. The former is a small but non-trivial issue with a metal tank. With a fiberglass or poly tank vertical conduction is not a significant issue either.
Except in the winter it's more likely that your tank is surrounded by water if it's at any kind of depth. Placing it vertically should reduce the wall-loss but it's still a lot of surface area. I've never seen a fiberglass or poly milk tanker, always stainless steel. Either way the "head" (where you lose most of your heat) would be the same size if the tank(s) are vertical.
I suspect you'll actually be ahead to use a single tank with vertical stratification due to heat storage in the ground around it tending to help you out rather than fight you.
Now that I've given it more thought, 1 tank would be better. If you had a bunch of air hanging out above your hot water you'd lose heat to the air...convection. The problem I was trying to fix (that wasn't much of a problem) rears its head in my half-baked 2-tank alternative. Way to go, self!
That said, I don't think you want the tank in contact with the ground at all. You'd want to insulate the heck out of it because any loss to the ground is most likely a permanent loss (since it's winter). Sorry for meddling...take it easy