Do a code scan first and see what you get.
There is no upgrade AFAIK electrically..
It sounds like your intermediate clutch pack has worn out. It is barely gripping, and cannot engage under load, but once the load decreases it can engage.
It is easier for the clutch pack to hold than it is for it to engage initially so this is a common first sign of problems. It is also possible that to get this feeling from an E4OD that is skipping second gear completely and going to third due to a worn clutch pack or a damaged intermediate one way clutch.
It will stay in first for the entire time it should be in second, and then go immediately to third. See how many shifts you get after the first gear change to determine whether or not this is the problem.