My suggestion is not going to meet your budget, but my "go to" remote for seniors is the MX-980 from URC. The resolution makes it easy for grandma to see and the buttons are in fixed positions so grandma can remember where they are. In addition, the backlit hard buttons are easy to see and get used to. The interface can be made to be very simple, since graphical remotes offer a "clean canvas" for someone to create a familiar look for the senior.

I know it's not at that budget you set. But maybe it's worth spending extra money so Grandma can enjoy her TV. Finding a good remote for a senior is very tough, and this is the best option I have when I run into a client who needs it, and it really seems to fit the bill.

Good Luck,
Vincent