Engines aplenty
You don't need wierd rockets.
An Airbus uses a V2500 - 27,000 lbs thrust for 2,400 Kg. You could have two main engines - CF24s at 20,000 lbs thrust - and two retractable AE3001s (9,400 lbs) for the same weight.
As a simple solution, put them at the back, around the apu (would you still need one?). I'm would guess there's enough room (although you'd have to change the tail surfaces and adjust the fuselage length to maintain CG).
Hybrid cars which use different engines for different phases, were ridiculous once for reasons of cost, weight, complexity, reliablity etc. Now things have changed completely.