Are you on the waitlist now? If so, I would wait. You'll be on the waitlist both now and until waitlist movement time regardless of when you send the LOI (unless they say they pull from the WL earlier).
Also, schools know that FA offers have not been sent out yet (most schools send them around the same time from what I can see), so I would think that your LOI will really be not viewed with much weight.
A letter of intent is promising that school that you *will* go to that school over peer (note: similarly "ranked") institution.
If you are really passionate and eager about this LOI, I would contact the FA office and ask them about how they match offers in a non-presumptive way (try your best not to come off as assuming you will get in, but with an approach that exudes more passion/curiosity about the school). With some answers, you can include the info you learned in your letter, which IMO will come off as you really being passionate about getting off the WL and really doing the work to make sure you are 100% sure, which is what a LOI is supposed to signal in the first place.