Yeah, the whole “what about people who want / need to rent because of their current circumstances” problem really is easy to solve.
Create a crown corporation (for those not familiar, a not-for-profit entity owned at arms length by the government) to handle all rentals, with a mandate to offer rents at a (very low) rate established by a formula that accounts for factors of property value (footage, amenities, location), population density and rental demand in a given area.
Then you make it so that only this crown corp is allowed to charge residential tenants rent. Anyone else who wants to make money off of their second properties and the like will have to sell them to the crown corp. Anyone like in the OP who wants to rent for some months of the year will enter an arrangement with the crown corp where the corp rents the property on their behalf at the rates established by the formula.