I have been reading about the hardware differences between the TI-85/86 versus the Ti-83/84 series.
The difference in how the LCD is coupled to the rest of the machine is interesting.

On the 85/86 the LCD monitors a memory area (you can tell it which area) but on the 83/84, the LCD must be fed the bytes. So the 85/86 LCD pulls data, whereas data must be pushed to the 83/84 LCD.

At first I thought this would make writing/porting games a pain (almost Atari-2600 like?) but I see that the asm shells offer functions to fast copy ram into the LCD. So emulating the memory mapped LCD. I see this has benefit of controlling when the buffer copy happens (less flicker) and presumably on the higher res color versions, the amount of ram space as well as the color layout.

Looks like Doors CS is the shell that people use nowadays?

It's useful to identify exactly which calculators you mean-- the TI-84 does not exist

Per WikiTI, both the the 86 and the (ez80) color 84+CE use an LCD driver to accomplish memory-mapped vram. The 84+CE's LCD Driver was actually faithfully documented quite recently by calc84! The 84+CSE has... problems because it uses the same push-to-LCD strategy and colors require a lot of extra bits (as you've identified!). For the 83+/84+, solid, usable LCD management strategies do exist. Clever people have written routines that manage to be fast and readable; I recommend taking a look at the relevant part of 83+ ASM in 28 days.

I have 3 TI-85, 2 TI-86, one 83+, and one 84+ silver edition calculators. I didn't realize there were no neutral 84 calculators.

Only 1 purchased brand new in 1992. The rest used.