The pictures help a lot. The 15" version looks like it has a DB25 connector with an RS-232 serial port. The platin on the 15" looks a lot smaller than the 30". How often do you have to replace the platin?
I think I see a lead screw to move the cutter head back and forth. Is the LS driven directly by a stepper or does it have some kind of gearing system?
https://www.amazon.com/Linear-Motion-Ball-Screws/b?ie=UTF8&node=350657011
This is an expensive part if you have to have it made. You can use an off the shelf part as long as it's the same length or longer. You can make your unit longer by an inch or two and just to get a standard part. The big silver rod like guides are off the shelf and gliding guide parts are available, but you will have to adapt them for your application. You can have the cutter parts 3d printed if you can make a mechanical drawing of what you want.
Some of the parts are going to be too expensive to make/buy one at a time. You will have to have some cash to buy them in hundreds to get a good price. Inventory is a never ending battle. If you don't stock certain parts, you may need them and find they have a 6 month lead time.
It's just a process of You divide the project into little projects and figure them out, one at a time.
Do you have schematics of the controller board? Or a picture that shows the processor part number? If it's that old, it could be 8088 or a Z80. It also could have an EEPROM with firmware that could be disassembled, and a source file could be generated so you could rewrite the whole thing to avoid copyright problems and places where you would want to change the code. Or just use it as a pattern to compare to so you know things like how many HPGL instructions it has implemented.
HP-GL Reference Guide