I did that, eventually. Pushed the party through to 3rd level. And everything is okay for literally one session, before...
The party gets to Kresk and decides they want to stop the Abbot. I give the party's cleric some divine intervention to say "maybe don't try to kill this guy outright" - and the party gets frustrated that they have to leave yet another adventure location because it's too difficult to change anything.
So I'm assessing that the party has explored the village of Barovia and completed the Death House; gone through Vallaki and basically did all the damage they can do there by putting Wachter in power; met with the Vistani at Tser Pool; spoke with the Abbot in Kresk. In frustration, the other "old timer" in the group (a 55 year old parent of some kids in the group) says "everywhere we go, it's like we're at least 2 levels behind where we should be."
And sure enough, using milestone levelling, the party should be at 5th level before their next planned stop (the Winery).
So at the start of the previous session, they went from 2nd to 3rd level. An hour into yesterday's session (and after that complaint), I just shrugged: "Level up. I guess twice."
So we're averaging a level of experience per 4-hour session. Upon reaching 5th level, the party of 5 characters steamrolled through the Winery. I managed to shave off a couple of temporary hit points, but otherwise, it was a slaughter: druids dying before they could take a single action, dozens of twig blights being destroyed in two rounds.
Guessing I just push them into Castle Ravenloft now?
Do I need to completely redesign 5th edition? Is it even a functional system? (Doesn't seem to be at this moment.)