DIY 'Poor Man's Process' with a Projector and Some Gels

We had a tricky shot where a character was supposedly driving at night through a neon-lit city, but we were filming on a soundstage with no budget for LED walls or proper process trailer work. What worked surprisingly well was projecting abstract, color-changing light patterns onto a large matte white seamless backdrop behind the car. I rigged an Optoma GT1090HDR short-throw projector to a C-stand, loaded it with some animated light loops I'd made in After Effects, and then used various colored theatrical gels (Rosco E-colour+ 116, 317, and a broken up piece of 119) taped directly to the projector lens to break up and further colorize the projection. We supplemented with an amaran 150c off-camera for some key light, and a few PavoTube II 30Xs inside the car for interactive lighting. What didn't work was trying to get any kind of realistic focus fall-off on the projection, it always looked too sharp, betraying its nature. We ended up embracing a more stylized, almost comic-book look, which fit the scene's tone, but it definitely wasn't a 'realistic' process. Do others have go-to techniques for faking car process shots on a tight budget while maintaining a sense of depth and blur?