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I would just call the lender and inquire as to their policies regarding monthly reporting and explain what you just did to us.
As far as increases to your FICO score, what was your before and after overall installment loan utilization? Increases from routine installment loan paydowns usually don't happen often. If you paid off the loan significantly causing your aggregate utilization to fall under (say) 8.9% I would agree with you that you're likely missing out on FICO points, but otherwise you may not be at all or very little if so.
That whole quarterly thing seems odd to me. I've personally never heard of that before, although perhaps others have and it's more common than I'm aware of. While I wouldn't think so, they may be willing to do an off-cycle reporting if you ask. It can't hurt to try.
As for your loan utilization, first, is that your only installment loan that's open? If so, it looks like you've taken it down from 100% to around 79% or so utilization. It's possible that there's a threshold at or about 80%, but if so the gain would be minimal, perhaps a few FICO points. The entire span from 100% utilization down to 9% utilization is worth about half as much as crossing 8.9%. So, if an almost-paid-off loan is "worth" 30 points, perhaps 20 are gained from crossing the 8.9% threshold and the other 10 are gained at (possibly) multiple points between 100% and 9% utilization. In a nutshell, the gains over that 90% span are going to be quite small.
I have a car loan with Ally and they update monthly. My car payment is due on the 5th of every month but they don't update the balance until the end of the month. I just checked my Experian and my last balance updated on 3/29. I made my payment on 4/5 but they won't update this month's payment probably until next week(maybe the last business day of the month). It has been continuous reporting every month since I've had the loan.

I also have an auto loan with Ally and can confirm that they report my balance every single month, typically pulling data on the last or second to last day of the month. I am not sure why they told you that they report quarterly - the only explaination I can think of is that the rep was confused, because Ally gives you a free Fico Auto score every 3 months (quarterly), and maybe this is what they were referring to. Either way, your balance should be reported every month.