I don't think that is a good idea. No matter how small we make the mesh there will always be some parts that are small enough to slip through. It would also be a rather major modification.
Here's my suggestion:
Remove the Honeycomb/Matrix box by droping the bed nearly to the bottom limits. You can then lift out the box and just use the bed without the Matrix. (That's what I do when I need to cut small parts and don't want to fish them out of the box when I'm done.)
Now place your material on the bed as far to the front of the machine as possible and raise it to focus on your material. With your material far forward on the bed you shouldn't have so much of a problem.
If that doesn't work, you'll need to use tabs. To do that, break your vectors in your artwork so they don't meet and form a continuous cut.
Don't forget to put the Matrix box back when you are done.