Those brackets you linked to (the first set) are the standard solution for putting a 3.5" HD into a 5.25" bay that doesn't have a front bezel opening. They should do the job fine, and if you really want to go all the way down to 2.5 inch you could stack the two sets, if you don't mind it looking a bit goofy.

It bothers me slightly to think the first time I used a set of brackets basically identical to those was probably over 20 years ago.