Well, I finally did it. It took me exactly two days (or 16 hours) to write a piece of code that would allow me to temporarily drop back to real mode, call some BIOS interrupts, and then go back to protected mode again. The fact that I use MSVC++ and the COFF object file format didn't actually help me, as I had to be quite inventive to work around the limitations of the COFF format.
Anyway. I have now used this technique to upgrade my console from 80x25 characters to a whopping 80x50! So one might wonder if this was worth all the time. I guess so, since I can now also switch to graphics mode, and get ACPI information, et cetera.
Look at this huge console! It seems like the VGA cursor suddenly stopped working though. I'm thinking of simply implementing my own using the underscore character, and the PIT timer.