5.7 TR6060 Starter alignment?

My guess:
My 5.7 used a plate between the block and bellhousing, similar to the block plate of a scattershield. It's about 1/8" thick, give or take. I have no idea if your setup uses a similar plate, mine was from an automatic. You didn't mention one, so I'll assume you didn't use one. Lack of this plate would effectively mount your starter closer to the flywheel, possibly not allowing for full disengagement. For lack of an actual parts manual, have a dealer look up whether your year transmission setup utilized a block plate. To test this theory, unbolt your starter and insert 1/8" stacks of washers on the bolts between the starter and bellhousing as a temporary test- if the "odd sound" disappears, I think you've found the culprit. Then it's just a matter of locating or ordering the plate, if applicable.