First of all, it's so sad that people take an Infamy hit just for upgrading to a new tier of ship. The way they implemented ship tier into the matchmaking algorithm was the wrong fix for the problem...
But since it's a thing, and because the every-two-week season reset is also a thing, then you're correct -- you don't want the double-whammy all at once, or you might risk hitting "tanker" status, which apparently = Max Infamy of all time - 800. ...which is another design decision gone wrong.......... but enough of these digressions.........
You asked when is the best time, so here it is:
1. As
@CaffeinatedChris said, don't even think about it unless you have good gear to put in the new slots.
2. Wait until you're on a high-cycle of Infamy. Meaning, if you generally oscillate between 2200-2600, wait for a good streak to put you on the high end of that range (like 2500+).
3. And then ideally, if you're on a high streak and think you can maintain it until you're 6-8 days into a given season, that would be ideal because it spaces out the negative influences as far apart as you can.
Prioriy is 1 > 2 > 3.
Good luck!
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