I've experimented with roe over the last few years, doing everything from butchering while still warm to hanging in a chiller at 3 degrees for 14 days.
With the exception of the very longest hang (12 days plus), nobody who tried the meat could detect any difference at all. Beyond 12 days, it got noticeably more gamey - you could even smell the change when butchering. That transition matched a change in the tenderness, with the meat suddenly becoming much more tender.
I really don't like the gameyness - it really spoils roe, which is usually a lovely sweetish meat. So I'm sticking to short hanging times from now.
I did also test different bleeding regimes, with similar conclusions: with chest shot deer, bleeding is a total waste of time. It makes precisely no difference.