LM2596 minimum input voltage question

Setting up parallel switching regulators is hard. They might not run in sync and start supplying each other. Also, you're saying you want 25A. You would need a ton of those regulators to make it work, if it would work at all.

My suggestion is to get some big coils and FETs that can handle currents like 30 - 40A and a buck-boost converter. Alternatively, you could begin with a buck converter and regulate to a like 10V, and then boost up to 13.8V again. Don't expect to find these regulators in a package that will supply, you'll have to add external components. Don't forget that a buck converter needs to handle 25*13.8/10 = 34.5A+ (not accounting effiency) , because the voltage is lower.

The converter is operating within its specifications. See the "Tolerance Envelopes" at the top of page 3 of the datasheet. The output is allowed to be as much as 10% high at 10% load, which could be as high as 6.6 V in your case.

Try other loads, up to 100%, and see if it generally follows the load line that they show.