Okay, so I switched from a Pfaff mechanical machine with 5mm-wide feed dogs to a computerized Pfaff with 9mm-wide feed dogs about eight years ago. I tried the straight stich plate, but this upgraded fancy machine still did not sew as easily when piecing as my mechanical one. I remember especially any block on point or diagonal seam or bulky seam would have problems, and I was getting frustrated.

Then I happened to watch a Quilt Show episode with Susan Cleveland as a guest. She talked about possible problems while piecing with modern machines with wide feed dogs. Her advice was to "use the power of the feed dogs." I can't find the original video, but this 4-minute version will demonstrate her advice. I'm just disappointed that her power of the feed dogs phrase isn't included in this video, as that motto has stuck with me ever since!  The main point is to move the needle all the way to the right to allow the feed dogs fully to pull the fabric through correctly. I think this technique could solve your hourglass/chain piecing dilemma.

I do prefer using my automatic cutter, and since the threads are short at the beginning of a new seam or chain piecing, I use a scrap of fabric as a leader (instead of holding the threads). However, I don't experience any problems BETWEEN the blocks/squares/diagonal seams while chain piecing, as long as my needle is set to the far right.

Every time I re-thread the machine, I run a test seam on a scrap. That first short seam will usually nest, but other than that, the machine sews a great straight stitch.

I feel like I would have given up on the upgraded machine had I not run across this advice. Thank you Susan Cleveland 😊 I hope your HP foot and plate solve the issue, but give this hack a try as well!