What your suggesting is going to be tricky to implement. First you can only add delay, not subtract delay, so your specific example will not work: you can not "rebroadcast at the drone's antenna" before the original signal reach the drone.

To overcome this, could record all the gps signals, and rebroadcast them with carefully timed delays. But than gps time as determined by the drone will be different from what a clock in the drone gives, so it could be detected. If you are quick enough it might work, but it's non trivial.

And if the drone uses carrier-phase gps measurements you have a whole bunch of other problems.

Not saying it can't be done, but it's not easy.

That would only work if it had a really silly default similar in a way to "automatically connect to available Wi-Fi network" even when it's unsecured. It's possible the manufacturer may have overlooked something like that, but if it is in a military capacity, I doubt they would have left a gaping hole like that. Electronic countermeasures have been in use for several decades now so jamming/hijacking etc... would have been considerations in the design and they may have introduced hardening against those.

I would hope the engineers designing the drone would NOT fall back to the unencrypted channels precisely because of spoofing attacks. I would think they would rather have the drone use inertial guidance to get it to a friendly area where its secrets would be safer. It may not be able to land without GPS but it would have prevented it from falling into "enemy" hands. Perhaps even activate a self destruct mechanism(s).