You will indeed need a so-called "co-term" contract for FortiGuard/UTM services since FortiCare and FortiGuard have to align in contract period.
But, that is no big deal. Co-terms are like 2% more expensive than off-the-shelf contracts but they have the distinct advantage that they are day-based. You could have them tailored for 365 days (=off-the-shelf), or 364 or 288 days...that's what they are for.
OTOH, if your current FTNT partner is not able to cope with such an everyday task, choose a different one. Wouldn't googling "Fortinet <mycityhere>" supply some offerings?
Me: FTNT partner since 2003, alas in Germany.
"Kernel panic: Aiee, killing interrupt handler!"