Hoping for a stroke of luck (Brit trying to stay in Taiwan)

Looks like the max is 180 days:

And no way can he keep renewing a visitor visa for three years.
OP, I’d advise looking into a third country to ride out this pandemic in.
Usual policy for overstayers is pay a fine and lose your visa waiver privlege for a certain length of time, thus needing to apply for a tourist visa in advance before every time you enter Taiwan.

Barbados has introduced a new 12-month visa for remote workers/digital nomads such as yourself:

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