Originally Posted by
nfmisso
This one will work well for your application:
https://www.amazon.com/dp/B0165T3AXI/
In my experience, much better than any Shimano for less than twice the price. I have used this RD for 5, 7 and 8 speed applications to date.
EDIT after re-reading your post.
You may also have a worn out shifter. If the 7 speed index shifter is original to your bike, it likely needs replacement.
I think that you may be on to something here. Older shifters can become sluggish as grease in the mechanism congeals over time. This particularly affects shifts from larger to smaller cogs. Incidentally, Acera derailleurs are fairly good quality and should function very well if other shift components are up to par. As well, and Shimano rear mountain bike derailleur designed for up to 9 speeds should work perfectly on the OP's bike