A fine set TCT blade which has been designed for the aluminium industry..... that's all you need and that's all a "special" acrylic blade is.... a fine set TCT blade for aluminium re branded and stuck in a "plastic saw blade box".
If your blade is chipping then either the blade is way too coarse (i.e, it has too few teeth) or, it's as blunt as hell.
If you blade is melting the swarf back to the sheet then it's blunt and cutting through your acrylic like a grinding disc does..... abrading rather than cutting and building up a lot of friction which manifests as HEAT.
There is NO big secret here... chipping is always caused by a blade which is too harsh with too few teeth and melting is always caused by blunt TCT teeth.
If you plan to cut a lot of acrylic you need TWO identical blades so you always have a razor sharp honed blade ready to swap the moment the blade in the machine starts to dull. This is the BIG secret to cutting any kind of plastic on any machine which uses a spinning metal tool... two identical tools, one sharp one knackered... the sharp tool ALWAYS delivers... the dull tool ALWAYS makes a mess.
As for the rotation direction.... the right blade which is kept sharp will cut just fine in the correct direction. Flipping blades is asking the back of your TCT blades to do the cutting.... they haven't been ground or sharpened to do this and the TCT blade tips have been cemented to the blade with the expectation that loading force will be applied to the correct face of each tooth. Flipping blades is dangerous because it can "ping" off the TCT teeth and will lead to nasty kick back which can catapult your acrylic across the shop floor.
The masking on your acrylic does not provide any lubrication.... it's there simply to protect from scratches.
Paper masking is an oddity exclusive to the US.... in Europe all our acrylic has always been sold with a plastic film mask like you'd find on alupanel. If
paper was better for cutting we would have changed over to it...... we haven't.