I have several different machines (401, 403, 301, featherweights, 66, 99, model 15 treadle and a handcrank). I love the 401 and the 403 better than any of the other machines. They are fantastic machines.
I haven't used my 401 or 403 for fmq so I can't give you any tips on how to do it. Things I would try....instead of putting the throat plate up, I would try covering the feed dogs with an index card (tape the sides of the card to the machine but make sure there is a hole in the center of the card for the needle to go through). I would also try fmq with a different type of bobbin. The newer plastic bobbins for the singer 400 series that they have at Jo-Anns can cause some problems because their dimensions are not always accurate... but then some of the older metal bobbins get a little worn and don't work as well either. ( I usually buy my bobbins from a lady on the net who restores and sells older singer machines and parts. She checks the dimensions of each bobbin before she sends it out to her customers. )
I was talking to a quilter one day and I was surprised to hear that she used her 301 (which is also a slant needle) on her machine quilting frame. She said that it worked great for quilting. In thinking about it, the 301 has a vertical bobbin whereas the 401 has the horizontal bobbin so that may be the difference. You can also drop the feed dogs in the 301. My point in saying this is that the it being a slant needle may not be as much of a problem as it having both the slant needle and the horizontal bobbin combination. I think I will try the fmq on one of my machines and see what happens.