I want to push back a bit on multiple LDOs in parallel. The "18650 Battery Shield V3" has three XC6206 3.3V regulators in parallel, with no diodes. The schematic is here:
https://forum.arduino.cc/t/18650-battery-charge-shield-board-v3/599068/16
I have a couple of these, but I haven't tested the 3.3V output under significant load. But many thousands of these modules have been sold, and I've never heard of a problem with the 3.3V output.
Of course the outputs will all be a bit different, so the regulator with the highest output will supply the load until its output starts to sag, and then the next one will kick in. At least I assume that's what happens.
Anyway, I would suggest that you test the original setup to see if it works. You just want to be sure they supply enough power, and don't get hot. I suspect it will work just fine.
You will not need diodes unless your regulators both source and sink current. Most LDOs just source current, so when the voltage is higher than they are set for, they just shut down. But you can test that with your meter. The only backflow should be a tiny current through the feedback voltage divider.
Edit: Instead of diodes, inserting a resistor in series with each output might help balance the current loads among the LDOs. I'm thinking very low value resistors, like an ohm or two. Or maybe a resistor only in the low-current LDO's output. If you're lucky, the output of the big LDO will be the higher one, and then it will supply all the current when it's enabled, with no resistor needed.