Some people use "accelerating" this way. It kind of bugs me, but I see it’s even made the NY Times (their venerable London uncle only has it once, in a quotation, but then, they are not exactly known for their modern, edgy language ...) .
To me accelerating means "gaining speed", so I read "accelerating interest" as a kind of ellipsis, meaning, as in #1, "interest growing at an increasing rate" or (in a transitive sense) "hastening the growth of interest."
That reminds me, it might be helpful to note that zunehmend does not have a transitive sense whereas "increasing" and "accelerating" both do. Sometimes this ambiguity can be useful.
"Rising" and "burgeoning " do not have transitive meanings.
Edit: burgeoning doesn't sound very modern or edgy either, though, I'd advise against it....