As a native American speaker, when I see British folk sign off "Cheers," I have always interpreted it as they are sending out a general well wishing. It does remind me of when Americans say "Cheers" when they click glasses in general goodwill to each other.
But more than that, whenever I hear a European say or write Cheers, I always think it sounds so cool ...
If you want simply to confirm to your professor that you have received a message, well received conveys more than that. Well received, which is sometimes hyphenated, means that something has gotten a good reaction or has been viewed with approval. For example, "The book was well received by critics." See Macmillan and Collins for examples of dictionary ...
What are the options that you tried? There are several variants to choose from. A few are:
It would mean a lot to me.
I would be much obliged if.
I would be indebted to you.
I'd appreciate it if.
I would be grateful to you.
Hope this helps.