What kind of system fits a Hotline Miami-style campaign?

Look for quick combat where a single hit can take someone out, and where enemies follow the same danger rules as player characters. That’ll do more for the brutal feel than adding lots of special rules. You can reflavor the setting around the system, then try a short session to see whether the pace feels right.

I’d check the online tools before settling on a system, since easy-to-fill character sheets are a practical part of running this remotely. Make a sample character and run a small test fight. If tracking damage or other details slows things down, a simpler ruleset may suit the campaign better.