Wouldn't a thermostatic type shower valve be a better solution there?
Old thread...depending on the design, many thermostatic valves will run all or nearly all hot until it needs to begin tempering it to achieve the desired set temperature. I have a Grohe thermostatically controlled valve in my tub/shower that I like. My first exposure to them was in a Holiday Inn in London, England where they worked quite well, which led me to consider one for my remodel. They tend to be the most expensive type of shower valve, but they are nice.
Important note - I'm not a pro
Retired Defense Industry Engineer; Schluter 2.5-day Workshop Completed 2013, 2014