The approach seems straight forward but I am not sure your current pot is going to accommodate your volume being only 22 qts (5.5gal) in accounting for boil overs and the amount of wort that will boil off on a full 5gal. boil. We do full boils and use a 7gal kettle with an average boil off of 1.25 gal/hr.
In addition not only are you increasing the grain but I am assuming the amount of extract as well with a partial mash so you also need to account for those volumes, using beersmith you should be able to re-scale your recipe and verify your equipment profile and run the calculations. The software will place a red dot next to any item that is out of sync and let you know where you will run short.
As for the method you are essentially trying to do a partial boil of a partial mash, similar to partial boils of extract recipes so assuming you have the proper capacity your theory should work in the dilution to proper OG. Another thing to keep in mind is that just because you want to double a recipe it is not always as straight forward as just doubling your ingredients as all the different ingredients are effected by temps, times, efficiency, etc.