Alaska Cruise

My friend and I booked a 2 week Caribbean cruise with Carnival over
three years ago, every year something has come up in the winter months
causing us to delay it to next winter. Now it looks like there will
be a problem this year too.

Carnival's Alaska trips don't have the same appeals as some of the
other cruise lines (Princess is the one we are looking at now). Does
anyone have reasons to recommend any other lines for the months Jan,
Feb?

We would like to budget less than $2800 per person.

Thanks for any suggestions, even if it is just to stay with Princess.