so from what im seeing here, an amplifier would be better than a bigger dish?
The question first has to be which is losing signal first?
The end of the chain is the receiver giving the 771 error.
If the dish still has a weak signal, that is getting weaker through the coax to the receiver and the receiver has fallen below its minimum level, then an amp can help.
If the LNB has dropped to the point it can't output a weak signal, then the larger dish is the only help.
The "if money wasn't a concern" had the larger dish, the SWiM with it's AGC [which is important because just adding gain can cause problems when there isn't rainfade] that will both attenuate the LNB signal in good weather and amplify as the signal drops, and then an amp, that also can't have too much gain, but would be used to compensate for the coax & splitter losses to the receiver. The receiver shouldn't have more than -20 dBm.