So I reinstalled Gmod a few days ago and found a mode called GMTower, with a mode called virus. It is exactly what you are all thinking, a game mode that for the most part replicates Virus from Timesplitters. A few selected soundtracks are in there with some similar weapons. The maps are one of the biggest differences, due to them being a combination of custom maps and replicas of CS maps. Also jump is disabled.
Its pretty fun and gives a lot of insight how this mode would play and feel like online with a large player base.
I would say the most annoying thing about this mode is the only mention of Timesplitters exists on the Workshop page, meaning a lot of people believe the idea is original to the mod developer. Kind of annoying but I guess that's usual with any franchise/genre that isn't a huge part of the mainstream.
Its a bit of a nuisance to install but I suggest you guys give it a try, it's pretty fun.
(Forgive me for any weird typos, I'm typing this from my phone)