The big idea is after doing the quest for the nether crucible, upgrade all your relic first tier so that you have a +15 ilvl bonus. It seems switching to another relic without upgrading the new relic will actually add a +10 ilvl to each.
Went from 935 to 942 after changing 2 relics (one of the same ilvl, one +15 ilvl upgrade). Weapon is now 1018 on warcraftlogs
I don't know if the actual damage is there or not, raiding atm, needs testing.
Posting in public because I really don't mind this being fixed.
My weapon ilvl shows 951 in game, 1018 in warcraft logs