As a very basic rule unstable people are not recommended to trip, I'm sorry. Some might argue that tripping can be therapeutic and turn your situation around. While that may be true there is also a very real chance that it will make everything that much worse, I definitely don't think I would risk that.
Zoloft also may reduce the effects of LSD (or other serotonergic psychedelics) but it is hard to predict by how much. It seems to vary quite a bit. To stop taking Zoloft (i.e. discontinuing psych medication) for a while in order to trip is another thing that is generally recommended against because it is extra destabilizing, see how that doubles up? Some people try to find a dose that is so high that it will overpower the medication but how does that not have bad news written all over it?
The only things I have heard about others I know on SSRIs say that psychedelics really made them lose grip too much and had non-specific / non-descript unpleasant side-effect.
How to stabilize? Well first the question is: why has your psychiatrist told you that about your serotonin levels? I take it he didn't measure them himself. It's associated with problems you seem to be having. Lower than average serotonin levels in the form of things like dysthemia are not really temporary, but on the other hand your depressed symptoms might only have a basis in something like identity issues, external factors that you can change and work on. Looking for those is your best path to getting stable.
My best friend has ADD and dysthemic symptoms and takes fluoxetine and mirtazepine. He used to trip with me with good results but meanwhile he kept having continuous mood issues and since he sought help he does not trip or take drugs anymore.
I hope this has cleared up a few things for you? What I tell you is just bits of info, I must disclaim: I do not presume to offer anything that substitutes for actual therapy. If you are from 1994 that means you are young, quite young enough to hold off and let things settle until you know where you are at. Your composure depends on how well you work on your issues and on how well you avoid things that destabilize you.
My advice is: better safe than sorry and wait a little while until you are at a point in life where you can more safely see where psychedelics take you. Plenty of time, don't worry!