Re: have you ever added weight to a fly reel...
Normally high sticking is done with a relatively short amount of line out. So most of the line is still on the reel. Therefore, I think it is the rod that is the problem. It is tip heavy to begin with.
I suspect you have already tried holding the rod higher up on the grip after the cast. That will help some when high sticking. If you have not, give that a try.
I think adding weight is best done by changing the reel to a larger size which will be heavier than adding weight to a smaller reel. If you have a larger reel for a heavier line weight, I would put it on the reel and see if it is easier to hold in high stick position. If it is, then buy a spare spool and put on the line for that rod.
I use a 10 ft 5 wt GLoomis GLX Classic matched to 3.9 oz. Ross Original Evolution #2. The original Evolution is a very light reel and this outfit is still tip light because the rod is extremely light. Have you considered that the rod and not the reel is the problem?
"Discovery consists of seeing what everybody has seen and thinking what nobody has thought"..........Szent-Gyorgy