I wanted to write up a tutorial on making plastic canvas items without canvas around the edges. It's something that I kind of taught myself, and it can be a bit tricky to explain without being there to show you. I will try my best.
Start by cutting out the pattern completely, with no extra canvas around the edge. Then take the floss you need for the outline color and cut it. I use all six strands for a fuller look, but use what is comfortable for you. I've found that the longer you can cut the thread the better, because you don't have to switch out the thread as often. The more you switch it the looser the stitches become, but it can be hard to work with until you are used to it. I also use tapestry needles which have bigger eyes to fit all of the strands.
The project I'm working on has black squares on the inside of the pattern, as well as the outside so I was able to attach the thread as I would with a normal project. When the color is only on the border, you have to be more careful but it can be done in the same way. I attached my thread by sewing over the tail end of the thread that way there are no knots to interfere with the backing. I use the same method for ending the thread by tucking it under stitches I've already done.
Once the thread is secured, you can move onto the edges. I normally do the edges first, but think about how the colors flow on your project. You don't want a lot of cross over on the back, so plan your moves wisely. Take the thread and wrap around one diagonal, then wrap the opposite making a cross. Continue as needed until you get to a corner. They can be tricky, but wrap as well as you can, even if you think it might fall off. You can never really pull too tightly on plastic canvas and I've really tugged at it some days! Again, use your discretion. Also most of the time if it does fall off, you can nudge it back on with your needle.
Once you're done with the edges, fill in the rest as you would normally. Once you finish I recommend gluing the edges so they won't rub off with wear. I use Mod-Podge glue, which you can find at any Joann's or Micheal's craft store. Use a small sponge brush, dab the edges and let dry. The glue will dry clear so if you're really worried they might come off, really glob it on.
Hope this helps, and feel free to message me with any other questions!