why does the solver want to shove 320% pot on the flop?

All options with the check mark are within 0.01 EV. Even the other 2 options are within 0.02 EV. So at GTO, none of the options are a huge mistake in EV.

The solver is very meticulously calibrated though. It is going to have the optimal value/bluff combos in the jam range and the response is going to be optimal, including mixing with the right frequencies with indifferent hands. One of the reasons solver will mix with the huge size and even prefer it here is in theory it allows us to bluff more, which maximizes our EV. We have so many hands that have a ton of equity, including unmade hands like ours that probably has over 60% equity vs big blind range, and up to 10 outs + backdoor spades when called.

In practice vs humans who cannot play GTO, one of these options is probably going to be best vs humans. We should generally try to pick the maximum exploitative strategy vs humans. Short of picking the perfect exploitative size for our hand vs a player's range, we probably want to simplify the solver strategy into something that is more implmentable by humans. IE, you pick one size for this board texture, either smaller bet with a higher frequency or larger bet with a lower frequency.

I would imagine we don't have to implement 3x pot flop shoves to have a strong strategy in practice.

I like the shove. In practice I have done this (and lost but it was Prague and I was the only one with 18 bb's and my opponent had 2 pair).

The issue here is that the board has JT in it. That means that there are a ton of straights that hit if we check or bet small (and are called). Yes we hit one of them but BB can hit the rest. So a 7, 8, 9, Q, A could be bad for us as would be a spade. Roughly over half the cards in the deck.

The other issue is if we bet 2+ bb's the effective stack size means that BB will shove all c/r's. Are we going to be calling? I don't like it really because I think BB would shove with some hands that would have folded to our shove. If they are balanced then we are in a -EV situation.

If we bet like 1 bb (the 16.4% solver bet) we have no FE vs any Jx, Tx, and 3x hands and any draws. This is a bet size I just don't like. It is basically an in position blocking bet which says we will likely be folding to a c/r especially a jam.

The shove gets a lot of draws to fold and the ones that don't fold we are likely ahead. It might get Tx and 3x hands to fold. It may look like an overbluff action but hands like PP's <= 99 will likely fold. And if BB has a Jx or better hand then so be it.

In the end the reason for the jam is that the more we are the aggressors the higher our chances for winning as long as we are balanced (and this is probably why its a 53% thing Solver-wise)