Going to 2 different players will not solve the problem. Lets just simplify things. Firstly your blurays will play at 60Hz since you can forget about trying 24Hz on your projector as thats outside of your specs. Secondly your DVD's if they are Pal will play at 50Hz, however since we are Region 2 , that encompasses Japan which is NTSC which is 60 Hz. Your player will be able to play both. Now to put a spanner in the works, if you dont have a region free player you will not be able to play any discs from the good old USA due to it being Region 1. However most bluray players are region free for dvd's but not bluray's.
To solve your problem, you need a player that can output a fixed refresh rate, either forcing the player to 50 or 60 Hz. That will create massive judder issues as there is no way to do a smooth conversion, most noticable on motion and panning.
Alternatively get a newer version of the HDFury and use its adjustable setting in terms of image shift on an RGB signal. This is more expensive and complicated as im not sure how many memory settings you have on your projector on a by input basis. You would then have to save the 50Hz signal into one memory bank and the 60 Hz one into another, so that the correct convergence , image size and position is retrived , depending on your imput signal.