Windows RT is not a supported mobile device. Windows RT isn't even a platform anymore, it got killed along with the surface 2. IMHO, anything that old is garbage and support should not even be attempted.
Windows RT was also notorious by not allowing 3rd party browsers (I believe at one point, the mozilla foundation was going to sue microsoft over blocking it), so you can't install another browser like chrome that would have better compatibility.
Unfortunately, I believe you've proven the device itself is most likely at fault. Fundamentally, it's most likely the way WinRT integrates internet explorer into the OS.
Google "Windows RT browser slow", there's a lot of results there you can point your client to and see if they can improve the device, but I would recommend advising them it's a discontinued platform that was never really meant for WebDirect, and point them to a number of newer alternatives instead.
Not sure if Windows RT had a RDP client available, but I thought I recalled surface users being able to remote on to a machine running filemaker pro and use it that way. Maybe that would work?