I feel so strongly like a 10-latency solution must be possible, but alas I cannot seem to find it. I'm submitting this on the first Sunday, which leaves me nearly a week to look for it, but no matter how many ways I try, everything is breaking. I suppose if you're reading this, then I failed. Though perhaps what I'm trying wasn't possible to begin with.

Edit: It's now 6 hours until the deadline, and I must sleep. 10 latency eludes me. Lower cost at 11 latency eludes me. I doubt this solve is any good, seeing as it was literally a day 1 solve, but it's the best I have. Maybe I just found something really good early on, but I doubt it.