This subject is starting to come up more and more lately. Review - first, RAF does not recommend a turbo charger on a VariEze or a Long-EZ. These aircraft, when operated within the normal envelope and at normal gross weights are probably the last aircraft to need a turbo charger. They are excellent high altitude airplanes having the capability to climb well over 25,000 feet. Turbo chargers and their associated parts are heavy, 20 to 25 lbs for an average installation. This is right on the tail, absolutely the worst possible place to add weight.
A turbo charger installation without a constant speed prop is self defeating. If you keep your standard prop, your engine will over rev at altitude. If you install a larger prop to take advantage of the additional horsepower available at altitude, your engine will not be able to turn up enough RPM static, and you will have marginal, possibly even dangerous take off performance. Remember your turbo will not help at lower altitudes. (unless you overboost a certain way to destroy your engine).
For acceptable take-off performance, you must be able to turn at least 2400 RPM static, (2500+ PRM Is better). Constant speed props are not recommended at all. Weight, complexity, initial expense, maintenance cost, and unreliability while running in the wake of the wing/ center-section are excellent reasons not to fool with these props. Use good judgement - the simple, lightweight, wooden, fixed pitch props have a good history and with care and attention to checking bolt torque at required intervals, can give long, reliable service.