I can't suggest a machine but I can make a couple alternative suggestions ....
I personally am NOT going to remove pins before they reach my needle. Call me lazy ... whatever.
I found three solutions to it though.
SLOW DOWN! The biggest problem with sewing over pins is that you are going to fast when you sew over them. If you slow your machine down you have far less chance of a problem.
Another solution is that I use very long pins and when I insert them I make sure the tip of the pin is outside of my 14" seam line. The pin doesn't have to be all the way to the edge when you sew.
Lastly, there is the glue stick. Run it along the edge of your fabric. Works great. But if you lay it on too wide (past the 1/4" seam line) then it's harder to open the fabric to press the seam. Not *hard*, but an extra step to make sure you have the seam fully open before you press.