I don't think this system will work well. I have tried a similar setup. The problem is that you will not get enough travel on the mainsheet.

The travel for the block that floats in the boom is no more than the length of the boom. If we say that is 8' the 4:1 primary will only travel 2'.

I had a problem with this when I setup my cascade system. My solution was to cascade 3:1 into another 3:1 giving 9:1. On your system you would get 10:1 because of the non-cascaded line from the traveler to the boom.

You will also find that 3:1 primary does not have the missalignment problems that macca pointed out.