There may be emulsions even when everything is done properly. How likely they are depends on many factors. The most important factors are a working TEK and then following it to the letter. Any even small difference can lead to problems.
Yes, particles can be one of reasons of problems. If you are having existing emulsion, especially for the first pull, your aim should be to break it up fully. You don't want any non-polar to be locked within it, because it holds quite a lot of mescaline and you would loose it.
You can use heating to break it, but mescaline freebase is not very heat stable and long exposition to heat is not very good.
If I had such emulsion, I would separate the emulsion + toluene first from the aqueous part. Then, once separated, I would heat it (toluene+emulsion) up for one hour with careful stirring every 5 minutes for 10 seconds. If the vessel has a stopper, it can be carefuly turned over few times instead of stirring.
If the emulsion won't break at least 70% by that time, I would stop heating.
The next step would be using time. Leaving it for few days can do wonders. It should be again carefully stirred or tured over few times a day. If you feel urge to skip this step because it lasts longer or speed it up, remember, this is not a feeling applicable to entheogens.
Once the emulsion breaks up, I would remove the toluene, join the aqueous parts, filter them as much as possible and continue with second pull.
Acceptance of the fact that our reality is not real doesn't in fact mean it is not real. It just leads to better understanding what real means.