The word "upmod" appears to be predated by phrases like "mod up" or "moderate up" (and "mod down" or "moderate down" referring to the reverse). "Upmod" and "mod(erate up)" seem to originate from the comment scoring system of the website Slashdot, which was referred to as moderation.
Slashdot introduced a voting-based "moderation" system in 1999
"Slashdot and CmdrTaco — the end of another geek era" by Mathew Ingram, says:
Slashdot’s “upmod,” a vote for a smart comment or thread, was the
dominant geek status symbol, a predecessor to the “digg” vote and the
Slashdot was founded in 1997, but the site's info page on "Slashdot Moderation" says that the moderation system was introduced some time after the site was established. The year the moderation system was introduced is given as 1999 in "Slashdot's 20th Anniversary: History of Slashdot", by whipslash (Logan Abbott), posted on Thursday October 19, 2017:
Slashdot introduced user accounts in the summer of 1998. "Ask Slashdot" debuted on May 13 of that year, with a question on potential ways to convince hardware manufacturers to be more compatible with Linux.
In 1999, moderation broadened from 25 editors to a rotating pool of more than 400 users. It was followed by metamoderation in September, which let the older user accounts on the site rate moderations as fair or unfair.
This timeline is corroborated by the posts here: Why do Slashdot's forums suck so bad?:
I don't find it a problem with the present moderation system; I just set Display Mode=Threaded, Highest Scores First, Threshold +2, and Reparent Highly Rated Comments. For the brief periods (15%) when I'm a moderator, I go to see the whole article tree and look especially (as CmdrTaco suggests) for 0 or 1 rated comments to moderate up. These settings have lead to a high-signal Slashdot experience for myself. [...]
-- Dan Hartung ([email protected]), October 08, 1999.
Overall, I find that with the moderation system, Slashdot isn't as bad as it used to be. I remember a long, long time ago when the amount of comments per article were much less, and the quality much higher. When it started going downhill, I found myself just not reading comments anymore. >[...]
-- Skrubly ([email protected]), October 08, 1999.
"Mod (up/down)" as a verb for "vote"
I found references to "modding" posts in this page of SlashDot .sigs from 2003:
"I'll likely get modded down for this but..." - Slashdot Karma Whores
“Usually at karma-cap, please upmod my troller account instead.”
The moderation system of SoylentNews, which uses Slashcode, uses the terms “modder” = “moderator,” “modding” = “moderating” = “voting on posts." It doesn't use "upmod" or "downmod," but “modded down” and “modded up” are used to refer to the comments that had their score decreased or increased by the actions of a moderator.