In this upcoming case, I actually believe Andersen should play the first game.
It's against Boston. He has had success against them in the regular season. They are the better team (although Pittsburgh is no slouch even though they are facing injuries right now), a division rival, and it gives him a full three days of rest before he has to go 3 games in 5 days against good Western teams (all away games).
I would close out 2019 like this probably:
NYI - Andersen
(1 day break)
BOS- Andersen
PIT- Kaskisuo
(2 day break)
VGK- Andersen
(1 day break)
ARI- Andersen
(1 day break)
COL- Andersen
(3 day break)
DET- Andersen
(1 day break)
BUF- Kaskisuo
BUF- Andersen
(2 day break)
PHI- Kaskisuo
COL- Andersen
(2 day break)
STL- Andersen
(2 day break)
VAN- Andersen
(1 day break)
CGY- Kaskisuo
(1 day break)
EDM - Andersen
(2 day break)
BUF - Andersen
(2 day break)
NYR - Andersen
DET - Kaskisuo
(1 day break)
CAR - Andersen
(3 day break)
NJD - Andersen
NYR - Kaskisuo
(2 day break)
MIN - Andersen
Kaskisuo is the first guy twice, and the second guy three times. It's going to be tough for Kaskisuo to get into games because we are playing some tough teams for the most part, and you don't want to give Andersen too many long gaps. His first game that would not be a back-to-back would probably end up being against Winnipeg in the first game of 2020, but I would likely try to get him into one of those games in the second Western road swing (likely against Calgary since they are in the middle) just so Kaskisuo doesn't go too long without a game and so Andersen doesn't have to play 8 straight games. Obviously that changes if Andersen is on a hot streak.