1. Pre-draft goalie prodigies hardly exist. Right now I think we have three goaltenders in the league that were drafted in the first round. The best goalie of this generation was drafted in the 7th round. Arguably the two best goaltenders in NHL history were drafted in the 10th and 3rd round. What the goalies do after they are drafted but before they hit the NHL gives you a much better idea of how good they actually will be. And you may not have noticed, but few goalies have done as well as Hellebuyck did in the time between draft and the NHL. Hellebuyck proceeded to put up above average stats in his first year in the NHL, after which yes he had a transition period (much like Lundqvist had a season where he put up a .912 sv%, and Price had a season where he put up a .905 sv% before they hit their primes). If Hellebuyck wasn't a prodigy, you must rest assured that his career at least sharply resemble some of the best goalies in the league. You did this before this season as well, where you kept bringing up Hellebuyck's draft position as if it actually mattered when he followed up his draft (which was his second draft btw, he actually went undrafted his first year) with putting up statistically
the best career numbers for a goaltender in NCAA history.
2.
@KingBogo pointed this out already, but:
Hellebuyck signed his first big contract ($6.167M per year with an $80M cap [7.7%]) after 166 games with a .917 sv%. Age 25.
Lundqvist signed his first big contract ($6.875M per year with a $56.7M cap [12.1%]) after 218 games with a .916 sv%. Age 26. Equivalent to a $9.7M contract for Hellebuyck.
Price signed his first big contract ($6.5M per year with a $70.2M cap [9.3%]) after 271 games with a .915 sv%. Age 25. Equivalent to a $7.4M contract for Hellebuyck.
More games, significantly more money. The question is if those extra games would tell us more about Hellebuyck's likely level as a goaltender, or if it just would drive up the price and bring him closer to UFA (again, if we actually were to go with your suggestions, we'd likely lose him in 2-3 years, or be paying him in the $8-10M range).
A Hot Goalie Isn’t a Better Goalie
Research suggests that a 3000 shot sample is when sv% starts to stabilize. If we were to ignore last year which you so gracefully suggested was a throw-away year because he needed to "completely change his game" to become the goalie today, we have a 30 game sample to begin next season to have a fairly good idea of who he is as a goaltender. Either way, he is extremely unlikely to dip down even to average starter in the league, which means his contract, which puts him at #16 for cap hit against salary cap at the time of signing is likely a good one.
3. The NHL doesn't allowed team or player option years, so that's a non-starter. Your other suggestion, that we simply sign him for two years and let him sit one year away from UFA with arbitration rights, is as much a non-starter. He would be able to do whatever he wanted in negotiations with another good year, which would kill us from a cap standpoint.