Well, I figured out what it was. Corrupt models for fbi and police4 from a pack I downloaded a month ago. Not sure how that happened, but it's peachy now. Isolated it purely to emergency vehicles (because that's all I've modified), and figured that maybe LSPDFR might be checking the core set of vehicles when you go on duty. Maybe so that it can add them to the police garage? Regardless, I found the problem models with that in mind. It was also made easier by seeing that OpenIV crashed when I tried to open the corrupted model. Thanks for the help, at least for the rubber ducky assistance. ✌️
OP, it might be worth going through and looking at the models for every police vehicle you have(or have modified) in OpenIV's model viewer, or just spawning each one of them in game. If the game crashes when you spawn a specific vehicle, it's probably good to look closer at it, and try replacing it. Since it's happening when you go on duty, I wouldn't be surprised if it's one of the core 'Emergency' vehicle models. This is anecdotal, but hope it helps.