If your machine can handle the bulk, I would keep using the 987 fleece. I used the even heavier fleece for my second bag and had no problems (I have a Bernina). I don't like the idea of trimming the fleece from the seam lines because IMO, that would debilitate the seams. I carry lots of stuff in my purse, so I would be afraid the weight of my junk would strain the seams if they didn't have the fleece. I also recommend a walking foot and for the machine trying to eat the ties, how about starting to sew not at the very start of the strip, but have your whole presser foot on top of the fabric. Your first stitch would then start about 1/4 inch in.
Love these purses, they are fun to make and the results are awesome. All of the pictures I have seen here are beautiful!