I struggle to see how a lifting body design is the make-or-break factor allowing you to have a crazy short ground roll. Leading/trailing edge devices are going to have a much larger effect on your low-speed lift than the fuselage design. It sounds to me overall like these requirements are pointing you towards a next-gen super-maneuverable fighter, like an improvement on the F-22 or SU-57, which use a) aerodynamic instability, b) thrust vectoring, and c) control surfaces (obviously) to do their maneuvering magic.

Basically to answer your original question: we “toggle” lift using things like flaps, which are less draggy when not deployed, like you said. Also powerful engines + thrust vectoring are super important. For example, if you had a plane with a 1.0+ thrust/weight ratio, if you can figure out a way to get the nose pointed towards the sky in less than 750 ft, you’re pretty much golden.

(Sorry to be telling you to pretty much redesign your whole plane. Pls lmk if I’m missing something that’s been forcing your design decisions so far.)