you can test for copper for sure. not sure on anything else. there's got to be a lab somewhere that you can send sample water to for testing. they do it for tons of other things(motor oil comes immediately to mind)
I'll do some digging, but I have no idea at the moment.
What types of toxins are you thinking? sorry I haven't been following any of the other problem threads so i don't know your issues
Run high quality carbon in your tank, in a proper reactor. The carbon will remove the allopathy. if your tank improves, you know you had corals releasing those toxins. Leathers and many mushrooms are considered known offenders of allopathy.
Before all that though, what are your tank's chemical parameters, and what tests did you use to obtain those data?
Are these your current parameters? (from the thread you posted)
pH-7.8
Nitrate-0
Nitrite-0
Ammonia-0
Alk-11
Cal-480
Phos-0.5
If so, I see some issues...
What kind of cucumber? I have one and I try to sight him often. If one dies in your tank it can poison the hell out of it...
Your Phosphate is very high, but you are right that alone should not cause quick meltdowns. Additionally some of your other parameters are off, which, in addition to the high phosphate can cause big problems pretty quickly. Your pH is low (should be aiming for 8.2-8.4), and your Alkalinity is quite high (you are aiming for about 9.2dKH-10.5dKH or so). Your Calc is pretty high, but I do not know that high calc is neccessarily toxic. What all this does tell me though-is that your magnesium level might be off (Too low). low pH, high Calcium, and High alkalinity are usually a sign of low magnesium too. Alk, magnesium, and calcium are all tied together such that an imbalance in mg, leads to an imbalance in all 3. First off, you need to determine your magnesium levels (you are aiming for 1350-1400ppm. You may notice an improvement once you get those parameters more in-line.
The reason I ask about the tests-this is important too-is that some test kits and methods are more reputeable, and of better quality, than other test kits/methods. If you used salifert, I would trust the results.
From personal experience with this same issue I would agree that you should check your Alk. MY zoa's, etc. would melt away quickly and in posting here and talking to people at meetings I was told to check Alk level. Well the Alk was extremely low and after raising it my zoa's and other corals were doing great.