I have done what you are doing many times and I haven't had any issues with stats or financials as long as the right check boxes are checked.
I always the below options checked.
Automatically adjust League Strategy
Import adjusted financial settings after each year
Automatically adjust league totals modifiers after each season for accuracy
Automatically import historical player-creation modifiers
I will say that I don't look at these things every year, especially finances. If the stats look good for the year, then I move on to the next.
I think if there were any issues with this stuff, it would have been found and fixed a long time ago. Just IMO.
Good luck!