I was asked this today and I have no idea of the answer.
"Is there a way to force my resolution on my laptop higher even if isn't supported?"
I can do a similar thing with an external monitor... I can select an incredibly high resolution and it looks terrible on the display, but it works. This is, of course, with a desktop graphics card and 24" monitor.
I did absolutely no research online. I am going to try installing various old drivers to see I can get any laptop to do such a thing. I tried to create a custom resolution using the Intel Graphics and Media Control Panel, but it said it wasn't supported. I want to hear your ideas as well as suggestions.