The brew-boss in-line GFCI would work, but I see 2 challenges with that approach. 1) It has L6-30 connectors on it, which will not fit either a stove or dryer outlet. 2) L6-30 doesn't have a neutral (white) conductor. Ok, one can "make" it work (by bonding a neutral bus to the ground in the controller although not legal) and depending on the application, you might not even need a neutral if you're not planning any 120 volt branches.
That said, I'm working on upgrading my current controller from 120 to 240. I'm planning to use my 30AMP dryer outlet as you mentioned. Now, the catch is this missing GFCI... Here's my approach. Using a 4 prong dryer cord, into a 50AMP Spa Panel (which has a GFCI breaker in it), and a L14-30 receptacle for the outbound leg to my controller. I'm upgrading the wiring in my controller to 10AWG to handle the increase to 30AMP. The 30AMP breaker in my house panel will give me overload protection and the 50AMP GFCI in the spa panel will give me the GFCI protection.
Another approach would be to replace the 30AMP breaker in my house panel, but a 240v 30AMP GFCI breaker is well over $100. I got the spa panel at Lowes for $60, the dryer cord from Amazon for $17, and the L14-30 receptacle from Lowes for $16. While it comes out to "about" the same cash outlay, the spa panel gives me portability to take my system anyplace that has a 4 prong dryer outlet (friend's house, new house, etc)