Smokers Haven sold more Perspex stem GBD's than anyone else in the world. Back in the very early 1980's they offered a liquid cleaning solution that they sold in a brown glass bottle like you used to get from a pharmacy for cough eyrup, etc.i purchased done then and it worked, as it was claimed to, on all lucite stems including Perspex.
When I was almost out, I discovered that this was no longer available. Apparently there were restrictions on sending it in the mail or by UPS that they didn't wish to deal with. It may or may not have been stocked in the store at that time, but if it was my memory is that it wasn't for long.
Fortuitously, at the very first Induana Briar Friars show I ever attended, which would have been no later than 1984, I met a man who had worked for Smokers Haven part time. He told me that the formula was very simple, 1/2 Acetone and 1/2 drugstore alcohol (back in those days, the only such alcohol I ever saw was 90 or 95% pure. I now see 70%,and 91% on the shelf at my Krogers. I use the 91% pure.
I have used this formula ever since on all Lucite stems, including Perspex stemmed GBD's that others have thought were stained beyond salvation. I have never experienced any cracking, hazing or other issues whatsoever. It works in a hurry, rarely requiring more than a couple of pipe cleaners saturated in it. I have never tried soaking the stem. Haven't needed to. Just dip a pipe cleaner in the bottle and run it through the stem.
If you don't want to use drugstore alcohol, you can use Everclear. I have, but couldn't see any advantage to spending the extra money. Oh, by the way,I get my Acetone at Kroger's where they have a 100% pure product sold as their own brand fingernail polish remover.
There are other things that might work for you. This works for me and has for over 35 years.