Short answer: YES, you will need endoscopy.
For liability issues, the doctors at your new hospital have to be able to "look inside" your stomach for two reasons: first to see if the mushroom tip has attached itself to the stomach lining and second to make sure the new tube is actually inside your stomach and not in between the stomach and the skin.
Most G tubes now use the balloon to hold it in your stomach instead of the "mushroom". The advantage of the mushroom is that it lasts much much longer than the balloon, at least a year and sometimes longer. The manufacturers of PEG and G tubes all recommend changing balloon tips at 3 months (button- low profile) to 6 months (tube).
The mushroom folds up easily so it can be pulled out. You can ask for sedation if you are worried I pass on it because I can't stand to sit in the recovery room for an hour. Besides my balloon has usually deflated in 5 months and my G tube just falls out and I've put it back in with bandages and tapes so the doctors have no issues.
The difference between endoscopic and fluoroscopic is that endo is done thru your throat while the fluor is like a live time xray. Both let the doctors "see inside" your stomach. No doctors will use endocopes on me because of all the surgical damage to my throat so I have to go fluor route.

Changing a tube is not a big deal at all, in fact, almost all the pediatric patients with a feeding tube have them changed by their parents and not doctors. It's just hard to change it yourself. GET IT CHANGED AS SOON AS POSSIBLE, leaks are bad business.
Keep the Faith
Charm