Even though DMT freebase can precipitate from a clean aqueous solution, I´m not sure DMT will precipitate from a crude aqueous mimosa decoction. It may be some impurities affect DMT freebase solubility (so you might have lost your actives or part of them if you discarded the liquid fraction).
If your alkaloids are indeed in your precipitated solids, then you could clean them up with any number of ways if you wanted. Any solvent that dissolves freebase DMT which can be filtered will further remove some impurities. If you are more comfortable with a class of solvents (lets say, ethanol for example), then you could try that. Dissolve, filter, evap. Repeat process if necessary.
Here´s an example of a method based on that.
As for whether petrochemicals affect the experience, I might be wrong but my hypothesis is that it´s more of a (conscious or unconscious) moral judgement you´re having that can affect the experience, and not something about the solvent itself. I once gave pure DMT extracted with naphtha to an amazonian shaman and he loved it, had very significant visions for him and felt he connected with the spirits. Not that his experience needs to matter, but it´s just an example. Another example is when when Maria Sabina took synthesized psilocybin from Hofmann and said ´the spirits were there´.
Some people in the ayahuasca/entheogen world argue that purified extracts ´aren´t spiritual´, which makes me wonder (in part sarcastically) about the solubility of those transcendental spirits we are seeking. Basically what these ´pro-natural´ people are saying is that spirits are water soluble but not soluble in non-polar solvents. What other chemical properties do spirits have? And if being ´natural´ is so important, why are they even doing an aqueous extraction in the first place? Why not just chew/eat the plant itself? There are indigenous groups that have historically simply chewed caapi vine for example, why not do that ?
Or, another way to think about it is: If it´s not about the solubilty of spirits, but about the bad karma that petrochemicals have, then do the spirits not care that petrochemicals were used to make the container the plant material is stored in or transported in? Or the petrochem as source of energy for transport or for the electricity where it was powdered or the source of energy for heating/boiling the plant before consuming ?
I just ask these questions as food for thought. Of course by all means you should do whatever you are more comfortable with. It is definitely very important that you don´t have negative thoughts before embarking on such an important journey.