don't discard your 'cloudy water', this is called an emulsion.
simply read the DMT extraction techniques (available at DMT-nexus or mycotopia) and begin at the "basified water/rootbark" step.
you need to get some naptha/heptane or toluene/xylene (be sure to test your solvent for purity by evaporating a small amount on a clean glass and checking for residue)
add a small amount of your choice of solvent to your basified water/DPT mixture. the freebase DPT will now be dissolved in the solvent. add a few extra drops of lye water to ensure complete reaction. if the emulsion persists, gently heat with a warm bath and add some table salt to increase polarity of the water phase.
with a syringe or turkey baster (or separatory funnel) separate the lower water phase form the upper organic phase. save the water phase just in case you mess up and can't find the DPT.
the organic phase should be placed in a clean flat glass dish and allowed to evaporate in a well ventilated area. place a screen over it to prevent dust, bugs, and small children from getting in it.
after some time, the solvent smell should be gone and you should be left with freebase dpt as an oil on the plate. place in the freezer to solidify it into a more waxy appearance for ease of gathering. enjoy!
lol at the Paul Mu'a'Dib reference, I often think about what a Spice trip would be like, I always imagined it'd be somewhere between DMT and Ketamine...but anywho, my understanding of the process, even the quick 'n dirty method is that it's not that complicated. If you cannot delay your gratification enough to wait a couple minutes to make your DPT smokeable, that seems a little problematic to me. Also, DPT is "ALL THAT" imo, or at least it has become one of my favorite psychedelics and I think experimenting with different methods of administering drugs can lead to qualitatively different experiences, for instance DMT. Smoking and IM injection are radically different experiences, so much so that for me, it is almost a different drug
Or dissolve in ammonia and let evaporate.