I think this is where the confusion is coming from. Goku was able to retain the SSJG power even after he lost the form due to time limit.
He retained some of it, yes.
As we can see he still fought evenly with Beerus even after he went back to base. Beerus even stated he didn't lose much power. That means Goku at base is now around SSJG level.
He contended with him briefly, which means his base is far and beyond what he was as a SSJ3 earlier in the movie, but he wasn't even his equal after going SSJ so how could he have been even with him at base?
I feel like everyone is forgetting that Goku went SSJ after SSJG timed out in BoG.
But Goku as a SSJG was. That's the point. So going from SSJG to SSJGSSJ is less than a 2x boost
I haven't argued otherwise. SSJGSSJ isn't an upgrade from SSJG; it's a completely different transformation... Which we know is about as powerful and more sustainable, but still separate.
Because it isn't now. After he became a SSJG he retained that power so he has it now even in base form. I think you are getting confused because you didn't realize Goku's base level increased so much
...Except even after he went SSJ he still wasn't as powerful as he was as SSJG, so your argument basically relies on SSJ Goku being ~Base Goku, which makes no sense. 😬
Also, I re-iterate:
Also, in RoF Goku is shocked at how massive of a boost Freiza's final transformation was, and outwardly admits his surprise. Now you're trying to tell me it was the lowest multiplier of all Frieza's transformations?