Have you tried Broken Machine with Depth just above full-CCW and Speed/Chaos very low? At that setting—right before the extra delay you mentioned in this thread becomes audible - you’ll get a slow, pronounced pitch-warble.
Volante can do tape stop like warble because it sits on a long delay line; the extra latency lets its virtual “read head” wander and create bigger tape-stop bends. Ribbons can run large internal buffers too (that’s how the extreme broken machine settings work), but once you go past a few milliseconds the lag is obvious and it becomes more of a wild rewind effect.
In short, every “delay-less” vibrato – Boss VB-2, ZVEX Lo-Fi Junky, whatever – still uses a small delay and slides the read head around. Very low-latency pitch shifting with intense pitch shifts exists, but the artifacts are ugly; listen to YouTube at 0.25× speed for a good example.
Dial in T1/T2 slowly and you’ll find the sweet spot: strong warble, minimal delay.