As a teacher can I sign off a generic letter to the parents of my class 'Yours sincerely' if I have addressed them as 'Dear Parent'? Or should it be 'Yours faithfully'?
There used to be very strict rules relating the salutation in a letter to the sign-off. Very few people now remember what those rules were, and even fewer care.
It was once my job to be correct in choosing between "Yours ever" (which is by no means as intimate as it sounds) and "Yours aye", and on one occasion at least in choosing "I am, Sir, your obedient servant" in preference to " I remain, Sir, your obedient servant".
If the only thing that the recipients of your letter are concerned about is your sign-off then you have scored some kind of victory. I would guess that the most important thing is that the substance of what you say should be understood. Those who oppose it will find ways of criticising you however you sign off your letter.