We spend the vast majority of our time in the clockworks practicing PVE content, so why not have a competitive PVE mode?

My suggestion is thus: Two identical paths, leading to a single, central area. These paths have the same monsters, same layout, everything. Each path has a separate team, and they are hostile to each other. The interaction between the teams at this point is limited: Maybe at a couple points, they are close enough for shots to go across. There is a switch you can hit that opens up a cage of monsters for the other team, or activates a trap. A split in the road, and whatever path you take is disabled for your opponent (so they have to choose the other one).

At the end of these paths is a single, central area, with a gate blocking the exit. To open the gate, the opposing team must be killed. So what is the advantage of getting there first? Healing pads. Not the ridiculously fast ones you find before bosses, but something like 1 health every 5 seconds. This makes faster teams gain an advantage (they get to be healed while they wait for their competition), and a linear advantage at that (more time for healing the better they do), but not an overwhelming one (if one team plays slow and safe, they will be near full health when they get to the end).

I would say leaving reviving in would be fair, because it is still 0 sum in terms of total team health. The random saves (an attack that reduces you to exactly 1) would probably have to be removed, however.