Well, I know that Flipswitch Games plans EmergeNYC to be multiplayer-compatible as well, with 32 players (police officers, firefighters and EMTs) playing in the same session, either in RTS or in TPS mode. However, the game is still in pre-alpha, even though the devs frequently update the game with meaningful patches, so I think this is something you should keep an eye on for 2018. I'll certainly do. :)
Excalibur Publishing also supports a similar title, called Flashing Lights, with the difference that this is planned to be a TPS-only experience, as far as I understand (and set in a fictional location instead of New York City). I'd be a bit careful with this one though, because Excalibur, as a publisher, has a notorious track record in abandoning their games (Euro Ship Simulator, Enforcer and World Ship Sim are just a couple of titles in recent years that they simply left to die). I'd wait for at least the early access start (due in 2018 Q1) and check the first Steam reviews on how serious the project looks like.
Police Simulator 18 will also support a two-player cooperative mode upon release.
Apart from these, I'm afraid the only alternatives left are the more complicated ones. You can either try organizing an LCPDFR session in GTA IV v1.0.7.0 (your best bet, I think), or delve into the modding scene of games that have police RPing aspects. You already mentioned GMod - other than that, I know that Operation Flashpoint (an awfully great, and awfully old favorite tactical shooter from 2001, currently called ArmA: Cold War Assault) and ArmA 3 have/had such policing mods.
In case of Operation Flashpoint, there was a pretty good, Czech Republic-based police package (Nogova Police Forces), with regular officers and tactical units, along with a wide variety of patrol and armored response vehicles. The downside is that you need to set up your own scenarios with the in-game editor if you want to use them to your liking, because the only mission I found that plays like a police patrol is this one. That said, you may want to give this one a try, as Operation Flashpoint literally runs on any PC, no matter your hardware, and you can find a lot of tutorials online on how to use the editor, or how to create multiplayer missions with this package if you want online RP with your friends.
In case of ArmA3, there is an RP mod called Altis Life, where I know you can play either as a civilian, a criminal, or a law enforcement officer. According to the website, this may be more in line with what you are looking for, the problem is that ArmA3 is pretty much of a resource hog, so if you have problems running GTA IV or GTA V on your rig, you will definitely face performance issues with this game, I'm afraid.
That's all I know, but I hope these help you out. Happy New Year! ;)