A quick glance at amazon.co.uk shows high-wattage induction cooktops that are relatively cheap, e.g. https://www.amazon.co.uk/GIONIEN-Domino-Induction-Hob-Electr... is a dual-burner 3500W model that takes 220V-240V (unclear if it's ok on 208V?) for £109.99 (USD$143). 60 Hz would be a leap of faith, but is probably fine.
Then we're back to having to upgrade an outlet in my house and wire it into the panel, which would cost $400 at least. And the only thing I'm getting for that price is more wattage, but not finer control over the temperature, so I'll stick to my current setup.
Not $50, but still.