Hi,
Really have to say, Bourns have some interesting app notes/booklets on using potentiometers/trimpots, and one aspect is using a resistor from V+ to the potentiometer, and thereby attempting to keep the wiper around the middle for reasons of safety, hate to go on, but trimpots are allegedly a bit feeble used as you intent to - if they go short, what stops a short-circuit straight to ground? That's why it's good practice to put the resistor.
All I can suggest is, I've also wanted to make the circuit fit the components from time to time, but it doesn't work. Even just a trimpot at the lowest end will have a small voltage across it so some of the 5V will be lost, all the same. Maybe using a step-up converter or a decent way of paralleling MOSFETs and putting the outputs in series or something?