I second, Third, and Fourth #eddie_roberts_jr
Think about holding a squat. Think about relaxing your legs. Choose some thought prevents you from standing up until your skis are all the way on top of the water. Standing up too early, and/or trying to get up with your legs straight, makes the whole thing much harder than it needs to be.
You could also try holding the handle with one palm up and one palm down: just like you would hold a baseball bat. It might be placebo, but I fell my grip is a bit stronger this way.
Lastly, if you are at a site where you have not been using a coastguard approved vest, try a coastguard approved vest. It's what you tried to do with the float but won't require spend the engergy to balance on the float while you're trying to keep yourself balanced in the water. (I've had friends out to the ski lake that couldn't get up until we swapped out a pullover vest for a CGA vest)