I grabbed some Acrylester "Pot of Gold" when PSI had it on sale at 2.95 apiece... I found that it turns extremely chippy and seems to be very brittle. In order to get a decent round surface for my chuck to grip, I had to resort to wet 220 grit sandpaper and sand off around half a millimeter to get a good clean round surface (backed with a piece of glass).
In order for me to drill my blanks, I turn them round between centers first, and then chuck them in my 3-jaw scrolling chuck. I then cut to length (for this stuff, I add 1/8th of an inch), and re-chuck the pieces I am going to use, face it and put a dimple in the center by hand to guide my bit. I drill with a bullet tip style acrylic bit, which I have found tends to reduce blow out at the end, but I don't have a 7mm version of this yet, so when I first made one of these I used the brad point bit and lost about 1/8th of an inch to blow out at the back end.
While drilling, I cooled the bit frequently, and used the lowest speed my lathe was capable of. I slowed down considerably towards the end, and it still chipped big chunks out at the end. I held the bit in a bit holder - hand held. It takes a steady hand, and gentle pressure, and a sharp bit is a great idea. To make my bit holder, I went to Harbor Freight and bought a corded drill with a hand tightening chuck, and removed the chuck. The chuck itself can't be attached to the lathe, but it fits quite comfortably in my hand, and holds up to 10mm bits... I still use this occasionally to drill when I just want a quick hole in the center and the final dimensions aren't critical yet.
While turning on the mandrel, I got the barrels as close as I dared to their finish profiles with my scraper, which didn't chip nearly as bad as my bowl gouges ... I re-ground my chisel profiles after this point to get better results, as the original profiles provided by Harbor Freight just weren't up to scratch. I finished the final half mm or so just using sandpaper, and graduated up to micromesh and Plast-X for the final polish.
I do have to say that the results of the acrylester is quite stunning, but it's a pain to work with all those chips flying up into my face while I work. I bought a face shield just for turning these plastics.
These days, I will turn these with a face shield and a fan blowing a good amount of air from the side (to reduce the fog in my mask and my glasses) ... I turn it at high speed with a carbide bit (2" radius) and take light passes till it's round. I now drill using a MT#1 drill chuck in the tailstock, but I still use hand pressure to push the bit into the work after I start the hole. I turn the barrels with carbide till it's close, though scrapers for larger curves works for me too ... still finish with wet sanding and Plast-X.