So from what I understand in terms of chemistry, would the following very simple extraction method work to some extend?

1) Take shredded (powdered) MHRB and put into a bucked of water.
2) Add hydrochloric acid to the bucked until the PH is low enough. (About PH 4??)
3) Shake a bit and let everything settle for a few hours (also boil this to help the extraction even more).
4) Filter off the plant material and collect the liquid (which should have a lot of DMT hydrochloride salt dissolved in it).
5) Add sodium hydroxide to bring the PH well above 8.68 (the pKa of DMT). This should cause the DMT to be converted
to the freebase and crash out of solution.
6) Filter off the precipitates, or evaporate off the water.
7) The precipitates should be mainly DMT (assuming the plant mainly contained DMT).

I guess, my reason for being interested in this is that it would completely avoid the need for a non-polar solvent. In your opinion would this work? If not, why wouldn't it work?

I doubt that this will work well.

The freebase crashes out in tiny particles, probably too tiny to be filtered.
Also, while DMT freebase isn't soluble in water, it gets soft/oily there and will most likely melt into the filter. At least it stays soft/oily until fully dry - idk what happens if you take dry freebase and add water.

So filtering the freebase out of the soup won't work i'm afraid. Evaporation won't really work either, because you'll end up with all the nonvolatile soup contents lye, tannins, dmt, ... It's also not fun to evaporate such amounts of water, especially when you have to take care not to heat too much (as you do with freebase).

If I were to try this, here's what i'd do:
- heat the soup (to ~60°C) after basification until the freebase particles combine to form puddles floating on top.
- let the soup cool to room temp
- put it in the fridge or freezer until the puddles harden up
- fish the puddles out using a spoon, fine strainer, something like that
- wash the collected freebase with distilled water a few times

This idea was inspired by this conversion tek, which works pretty well.

It's very well possible that this won't work, eg. the particles might not float to the top because the lye soup is too thick.

It's an interesting question, please report about any experiments and results

Thanks for the tips!

There's no reason not to use a non-polar phase to collect the DMT. Even (plain) paraffin candle wax will do. Backsalt the DMT from the wax with HCl and the resulting solution should give clean freebase on re-basing.