Alternative to "let me know"
Solution 1:
It will be easier to replace "let me know" if we use the substitute to replace "reply". That information is probably redundant since compliance with the request would require a reply of some sort anyway.
If we do that, I think "notify" works well in this context because "notices" are a very formal method of informing people. It can places some special emphasis on the textual nature of the correspondence, albeit without strictly requiring a textual reply. As long as I have mentioned it, "inform" is another good word for providing knowledge as well.
Here's a minimal change from the initial example:
Please notify me with what day/time works best for you if are still interested, if you need a later date, or if you are no longer interested.
As an aside, it seems like you have a prearranged date, so I would suggest also considering:
Please notify me if you are still interested. If you are interested but need a later date, inform me with a later date & time that is better for you.
I personally prefer the more elegant appearance of the ampersand, over the utilitarian look of the slash, especially in the context of an invitation. I also think splitting the rescheduling from the interest check with a separate conditional sentence also makes the sentiment a little easier to parse, one bit at a time.
Linked Resources:
Most definitions are retrieved from the American Dictionary of the English Language by Noah Webster, 1828.
rsvp. (n.d.) American Heritage® Dictionary of the English Language, Fifth Edition. (2011). Retrieved from The Free Dictionary by Farlex.
Berkley Construction Grammar Lecture Outline #7 by Professor Charles J. Filmore of The University of Berkley.
Solution 2:
Be positive - assume they are still interested. Emphasizing disinterest will make them start to wonder if they should be disinterested.
What date/time would work for you to ....go over this, meet and discuss...or whatever it is that you are trying to do.
Solution 3:
Question: "How would you like to proceed?"
Comment: "Please advise."
Directive: "Awaiting your reply."