My gorgeous gossies came from another forum poster, aged a few weeks and separated on the day I acquired them from their wider goosie family... So definitely not imprints!
I kept them penned for a number of weeks, as we'd been having a few fox / buzzard issues with my hens and I wanted to be sure they were of a fox-proof size before allowing them free-range.
They were in a pen we moved at least twice daily so they could get at fresh grass in the run.... I had no idea how prolifically young geese poo!!!
Yes - I agree with you entirely; impending death (you'd have thought) each time we went anywhere near, changed water, moved pen, gave food to etc. What a racket - and they all clumped up in one corner of the pen and shrieked their little heads off.
Since they've feathered up (mine are a bit older than yours and are Toulouse / Embden crosses) and been let out, they're the calmest most docile geese you could imagine. I can herd them anywhere, easily, and they don't bat an eyelid at anything; even being scooped up to plonk them somewhere else when they've wandered out of their (quite reassuringly small) comfort zone.
So hang on in there; the paranoid gosling stage seems to pass when they get bigger and more adult! Mine are now fulfilling the role I acquired them for - guard geese. They're perfect with me and my Hubbie, mix well with other poultry and my guinea fowl, but are proper little guardians of the smallholding if they sense a stranger in their midst.
If their attitude towards my own terrier is anything to go by, the fox won't stand a chance; four huge geese standing on tiptoe and not afraid to make a noise, bat their wings and give a well-aimed peck where it's deserved.... (Poor wee dog is a bit perplexed).
So just try to ignore the squeaking, shrieking stage - it's disconcerting and you wonder what you're doing wrong. They'll come right in the end and you'll be rewarded with some really super adult geese who'll hopefully become a very valued presence on your holding.