We have found a property manager but will keep RL in mind should we need an alternative. 

Or an alternate strategy if your goal is to have a vacation rental paid for is to buy some sort of investment, STR, buy and hold, stocks, bonds whatever and just dedicate the cashflow from that to renting a place each year. 

Other alternative is to move to cheaper area (CA->TX or bay area->sacramento/vegas) ; but that would reduce my cash position!

They suggested an alternative method, but I would need to provide more information, like passport, which I refused.

Alternatively, consider partnering with a cash buyer or exploring other investment strategies like turnkey rentals.

Alternatively you can simply wait a month or two as the person will likely start relisting the property on those websites once they feel like its safe to do so. 

This would permanently damage the window, and so I'm looking for an alternative.

However, this option is considerably more expensive, typically costing 5 to 15 times more than the alternative.

A private loan or rich uncle is another example.The alternative with a mortgage is that you have to BRRRR sequentially, not in parallel. 

Alternative options include a cash purchase, requiring significant upfront capital, or a hard money loan with higher interest rates.