I've had to deal with this all the time in Tortured Planet. Even now, you can still see a couple of slime trails in scattered places (the most severe ones being in the underground lake room in Sunshine Atoll Zone Act 2 and the very first asteroid field of Spacewalk Zone Act 2). For every slime trail you see in my levels, maybe ten or twenty more were painstakingly wrestled out of existence before I threw up my hands and decided that a particular one was the least bothersome.
The core cause of this problem is that the nodebuilder doesn't always build structures exactly as they are in SRB2DB. Sometimes they have to round off on distances, which tends to create openings and leaks in sectors that cause slime trails and HOMs. This problem seems to be further exacerbated by copious conjunctions of "invisible Thok Barriers" (Thok Barriers with F_SKY1 as both their floor and ceiling) with regular Thok Barriers. Ultimately, it all boils down to one or two vertices that were put in unfortunate places in your map. That's a bigger problem than it sounds; it's pretty much impossible to predict what configuration will cause problems until you've built it and tested it.
I have a pretty ironclad 5-step method for trying to get rid of slime trails:
1. Determine the direction the slime trail is coming from (in other words, which way you have to look to see it.)
2. Look at your map and work out a "slime trail vector" based on what direction that corresponds to.
3. Regard any vertices close to the vector as suspect.
4. Play around with those vertices. Move them in different directions, attach new sectors to them, remove existing sectors, etc., each time testing the level again to see whether any of the modifications shrinks or eliminates the slime trail. There are all kinds of things you can typically try, so test every possibility you can think of.
5. Eventually, one of the things you try will either make the slime trail vanish or become less severe. If it is entirely gone, well, pat yourself on the back. If it's just a little smaller, then take what you did before and make it more pronounced (that is, if you moved a vertex 32 fracunits up last time, move it up another 32 fracunits and see what that does). Repeat as necessary.
It's a fair amount of work, but it is pretty much the best method I know of. I hope that helps!