maybe i can have the surgery fail and than hiccup panic swallow an egg or something

if he's made aware that the eggs even are a solution

We can handwave Garrett telling Hiccup about the various methods available since they talked about Hiccup having a parasite...

...and Garrett eavesdrops a lot so it's pretty reasonable he hears things all the time.

aah yes, thank you!!

(In canon, he knows everybody's secrets. He reads diaries and eavesdrops all the time. XD )

W O W garrett rude

Look, it's his thing okay.
He just happens to be in the right spaces at the right time to hear all the gossip. (Yeah, he's horrible.)

maybe he should work extra as a journalist haha

Phfffft.