You don't need a fancy solution to randomly add latency -- just do what I did and sign up for Cox Internet.
I've heard the latency can be as bad as 3 days depending on how strong the wind blows.
This is the trap that so many fell into when they ditched DSL for CPL (Carrier Pigeon Line). The price was right; the bandwidth was _incredible_ (1TB packet sizes!); and the latency, bad as it was, was something you expected and prepared for. What's easily missed, as you pointed out, is the variability of that latency. If the wind is in your favor you'll have the latest copy of the internet downloaded in one or two days, unlike those plebs on fiber who have to spend weeks downloading the thing. But one strong headwind later and you'll be spending your time reading the x86 reference manual* for the hundredth time while you wait.
* Fun side fact (as if this comment was enough of a tangent already), you used to be able to request a _free_ physical copy of the x86 reference manuals. Not sure if that's still the case, but younger me was _thrilled_ when I found out and received that small library in the mail.