Interesting to see this now, not sure how I missed it, unless I just wasn't around that much then,,,
But from your first description of the trans not downshifting into 1st gear at stops, and starting out in 2nd gear, I had this happen for awhile with a '94 Silverado with a 4L60e trans, right after rebuild.
It wouldn't always downshift into 1st gear at stoplights and would start out in 2nd gear, but would usually shift down real quick a very short time after hitting the gas to accelerate.
Didn't like it, never did anything about it, it eventually stopped doing that, but then 2 years later I blew it up pulling a Ford 150 on a couple hundred mile trailer transport.