2. Mechanized Warfare can only affect a damage event once and add 1 damage to it, it doesn't matter if the source is both an artifact and red. A source either qualifies for its damage to be raised or it does not, it can't qualify or be affected twice.
Private Mod Note
Rollback Post to RevisionRollBack
I'm a former judge (lapsed), who keeps up to date on rules and policy. Keep in mind that judges' answers aren't necessarily more valid than those of people who aren't judges; what matters is we can quote the rules to back up our answers. When in doubt, ask for such quotes.
Unfortunately not. Now if the damage boost had been written as two separate abilities, one of which pumps red sources and the other pumping artifact sources, the Goldhound *would* indeed deal 3 damage, so that is something to keep in mind for the future.