There are some large button remote around, but most are very simple, and I don't know if they would work like a Harmony using Activity Based control. i.e. "Watch TV", "Use HTPC", etc. can be activities that turn on the appropriate devices and set the correct inputs and outputs for those devices.
NOTE: I just found out that the Harmony 350 is NOT an Activity Based remote, which is for me the main advantage of the Harmony remotes. So I can't really recommend it anymore, although they say it will control up to eight devices. I just don't know how it works. So the 650 it is then.As an aside, Logitech seems intent on destroying the Harmony idea and product line. Numpties.
They have a much broader range of offerings in America. The more expensive units have an App that you could probably use on a tablet, hence a large display. But I haven't read enough about them to know if they are just too complex, or even exactly what they will do. Some are aimed at home automation rather than simple Theatre system control.
My glasses are getting stronger and stronger as well. I pretty much use my remote by feel. I'm sure Hubby could as well once he has learned it, although the screen on the 650 may present some challenges. But if you are willing to do some setup you could have different colours on the screen for different functions.
While it may sound silly, once you have the remote you could take a picture of it then edit the image to add large labels. Then take the image to Officeworks and print it on an A4 or even an A3 sheet and laminate it. Hubby could then use it as a cheat sheet until he learned where all the buttons are.
Also take a look at this site. American, but you may find an idea, or they may work in Australia.
http://www.bigbuttonremotes.com/Or how about Voice Control. Only one big button required.
https://www.tomsguide.com/us/savant-universal-remote-control,news-21714.htmlI think Sony has some decent multi-device remotes, but I haven't looked at them.
Really though, I haven't looked hard for ages, because I just keep fixing my Harmony 880 remote. Still going strong years later. Original rechargeable battery and all.
Otherwise, Google is your friend.