Just rescued this 1987 NEC from the trash.....sign on the set said "in working order, free!". They lie! :mad:

Anyways, sound comes in, but the raster only takes up about the middle 3" of the screen, telling me that this set obviously needs a vertical height adjustment. How does one accomplish that on a set like this, if even possible? I removed the back, and all I see are convergence adjustments.

It most likely needs the caps replaced by the vert. out chip. Also check for cracked solder connections on the pins of that chip too.
pm me as I have the same model and can walk you through it.

Since I never yanked a PC board on a set like this, to what point on the chassis do I discharge the picture tube?

You shouldn't have to remove the board to do it. once the back is off you will have access to the bottom of the pc board.
First inspect the solder connections on the chip, And if necessary resolder them. If the vert is still short pm me and I will give you a diagram of the caps to replace.

You don't need to discharge the CRT unless you have to remove the HV connector. If you do have to, just slide a screwdriver that's grounded to the aquadag coating under the HV connector. I usually just use two long screwdrivers (one touching the coating and one to slide under the anode cup).

I'm not exactly sure on how to fix the problem here but I do know that i'm sitting in my grandmothers house right now and she has the exact same T.V. you picked up and it works like a dream. She's had this old thing for forever. Anywho, if u do get it up and working, I thought i'd drop the link here to the exact same remote that the T.V. came with. This guy sells them and i'm not sure if they're in stock or not but if not he has a link on his page to another guy that sells them. Anywho, here's the link and have a good one :) http://www.replacementremotes.com/store/productdetailp.cfm?productid=6237&categoryid=66

I can mail the schematic showing which parts to solder, if it would be useful. I think I even have a used remote.
Solder ic 401. replaceC413 1000uf 25v, C415 1000uf 35v C408 100uf 35v. VR 401 is the height control. Ic 401 is AN5521 if it turns out to be bad. If pin 6 measures less than 27v, then the caps are bad, not the ic.