The commercial acrylic cements such as the Weldon line are indeed mostly methylene chloride, with various additives to fit the application the formulation is meant to serve. In the case of the thicker cements, there is generally some acrylic monomer added, to achieve some level of gap filling, but in most situations where the edges have had a quality edge cut done by a knowledgeable fabricator, a straight solvent bond is the best approach. From my own years of experience in plastics fab, I have found that a 90% methylene chloride/10% acetic acid mix works well, where the acetic acid is a sort of flow agent to allow capillary action to work better. The commercial cements also work very well for general-purpose bonding, and are my second choice if I don't have the raw materials for custom blend. The other solvents, such as toluol, xylol, and acetone, are ones I would only use out of desperation. They are extremely ineffective (= slow), relative to any formulation employing methylene chloride.
A saw-cut done on tablesaw with a 60-80 tooth triple-chip ground carbide blade is my preferred edge treatment, and works very well for almost every acrylic and polycarb joint, including highly cosmetic joints such as museum display case work where the joint is totally exposed. Where I have been in a position of trying to make a fabricated solvent-joined box look like a molded box, I have flycut the edges to be cemented prior to joining. The setup for cementing and timing the solvent work cycle is key to what the joint looks like when complete. The edges to be cemented are NEVER flame-polished though, as this would lead to immediate crazing of the edges and adjacent bulk material. Flame-polishing can be employed on edges that are NOT to be cemented, though, as a fast method for applying a finish over a properly scraped or sanded edge.
The TAP Plastics video is a decent basic explanation of how to do it, but you can always refine the basic techniques to get a better job.
For poorer fit-ups the gel formulations can work.
