So I bought an even bigger 240x128 LCD (40x16 text mode) with a chip similar to T6963C (seems to be fully comptatible) and was pleasantly surprised that it works (almost) out of the box.
I had to break a jumper (JP3) that connects FS (font select) to ground in order to be able to select a smaller font. This seemed to be a common trait in those displays, as both of mine had this kind of jumpers.
Other than that, all my code that I wrote for 240x64 worked without any changes (except changing row count to 16 in my software). Both my 240x64 & 240x128 support dual text & graphic modes, however I haven't tried drawing graphics yet.
The screen is rather big and is around 11cm tall (1cm taller than my 20x10 cm SBC). It seems to work perfectly @ 2 MHz (I'm underclocking my bus via ATF16V8B when LCD/EN is asserted).
Also, /RD & /WD are separated (as opposed to HD44780).
Finally, potentiometer needs to be wired to GND/V0/VOUT (VOUT is a dedicated -10V pin), as opposed to HD44780 GND/V0/VCC.
I still find 240x64 (40x08 text mode) sufficient for my needs, and it also exposes some important parts of my SBC (like ROM ZIF socket & pin headers). However, this 240x128 display might be nice for some notebook-style build, like mounting it at 45° angle. I really love LCDs, I use them as my primary output device. They also make the SBC more standalone and give it some TRS-80 Model 100 vibes, and they also save me from having to figure out a video interface.
EDIT: There are 44 pins total (actually, 66 if you count the surface pads as well), but they are just same 22 pins repeated. When buying them first time, I was afraid that there wou;d be 2 separate controllers (some LCDs have two controllers for left/right half of the matrix), but this one is actually a single-chip display.