Hound dog was interesting

It’s difficult finding specifics on the F-16CJ. Internal fuel is 6970 pounds. External fuel can be accomplished many ways.

Centerline can be a 300-gallon fixed tank with optional wing tanks of 370-gallon capacity.
Or option for two 600-gallon drop tanks for ferry flights. Optional 300-gallon centerline tank in this configuration.
The CJ does not support the removable conformal fuel tanks.

Fuel consumption numbers on the web are all over the place with the crazy notion peak endurance for an F-16CJ is attained at Mach 1.4 at flight level 360. That sounds crazy. The manual cites Mach .87 optimally for 5000 pounds or more fuel above FL 400. It drops to Mach .45 at sea level and under 2000 pounds remaining.

Fuel is under eight pounds per gallon. The FJ-44-4 would need a weight offset of 90 gallons, not 148 gallons per engine. And it puts out an advertised thrust of 3500 pounds st. The engine can get you up to Mach .85, whereas you said Mach .77 was the limit. That’s perhaps the design speed of the Citation, but that isn’t necessarily the limit of the engine.

If you have an F-16CJ with a 370-gallon equivalent powered drop tank you could conceivably get away with a 2500-pound static thrust FJ-44 at 500 pounds dry weight. That would offset around 70-80 gallons of fuel. That 2500-pounds of dry thrust is at .45 SFC as opposed to the F100’s .90-ish SFC. That’s approximately a X% boost in cruise efficiency at worst. It may be up to Y% but I’m only guessing at F100’s best cruise setting. And. the boost comes at the mere cost of 20% of the fuel in the external tank, which the FJ-44 can still cut further into the efficiency curve by continuing to burn internal fuel.

That’s a substantial boost that only grows with a larger FJ-44. The offset of fuel is more than made up for in the efficiency boost.

edit: My X% and Y% off by quite a bit after review. At best it might gain single digit boost over the fuel offset in the drop tank. Well, after further review it doesn’t work out so well on the 370-gallon tank. The SFC of F100-pw-100 is .76 and the newer versions go up to .745 sfc. That puts a big hole in the plan for a smaller tank. You need the 600-gallon tank to approach much gain for a large investment in time and energy.