We bought one from signeer called a Signsaw Pro. Came supplied with a fine toothed blade which made a nice neat cut but a tremendous mess. Even with the vac attached everywhere was covered with particles of dibond. Changed to a Keencut cutter which is much faster with no mess.
check your local gumtree or eBay etc and get a second user foot pedal or automatic guillotine/shear. we have used them 25 years now and you just can’t beat them! we started with a 610mm wide one and then 4ft wide, now have 3-metre automatic one. you can pick the 4 foot pedal ones up for £100+ second hand.
Not the best video i could find, but this guy using one to cut steel sheet, but composite is soft and cuts like butter. Its not just about making a cut, if you take all your off-cuts of material lying in the corner you can quickly make them all squared up into usable sizes. and when it comes to lots of signs up to 4ft square, you can easily knock them out with perfect clean cuts in seconds every time.
Note: his foot pedal looks like a knocked-up one and is too high. they tend to be lower and a proper pedal section. if you get an automated one its much better, just tap your foot and it cuts.
we have a bench chop saw and ide never use it for cutting things like composite. as you say, makes a mess!