Welcome to the site!
I can see your dilemma, and in the future I would tag this type of question with "register" and "formality," just to be clear.
It is true that sometimes we couch statements or questions in more formal or polite language in certain circumstances, and yours sounds like one of those situations. I would certainly not use FYI in certain formal writing situations. Perhaps one of these might work:
I'd just like to bring to your attention... + an issue / a recent discovery / an interesting fact
I would just like to update you on...
I'd like to notify you that...
ADDED (based on poster's request for shorter expressions):
Two strong candidates for shorter expressions that are highly synonymous with FYI:
Just so you know...
Just so you're aware...
My only hesitation is that you indicated that you want to convey some respect, and politeness in English (and many other languages) is conveyed - in part - by lengthening and indirection (with modals, past tense, hedges, and hypotheticals). For example, if I want to know what time it is, I could just ask "What time is it?" However, that might sound too abrupt if I'm speaking to someone I don't know or to someone to whom I should show respect. But I could say:
Do you know what time it is?
I was wondering if you have the time...
Would you happen to have the time?
Or, if you want to get almost sickeningly polite, you could try:
I'm terribly sorry to bother you, but I was wondering if you happened to know the time.
The excessive verbiage serves an important sociolinguistic function.