The best solution is to live trap, get someone to neuter cheaply, then release the cats where they were captured. This keeps the niche full of cats for a while, so other cats don’t move in to take their place. And eventually the cats die off due to natural causes.
A very effective technique for a cat roundup is to get a female in heat, which will bring a herd of un-neutered males around for live capture.
That sounds like the makings of a steel cage match to me! Let's get ready to RRRRUMMMMMMMBLLLLLE!
In all seriousness, though, the problem is good old country doctor type vets that will neuter a male cat for $5 and a female for $30 are gone. It's become far more lucrative to cater to people with Pomeranians they carry around in their purse... and charge them $750/visit to find out the thing has worms.