The easiest way to reduce the impact of interest rates will be to convert debt to equity by (i) private placement at discounted prices that are 'unfair' to retail investors, (ii) rights issue/preferential offering. Those who have been investing in REITs long enough know that some REIT managers like to do (i), some like to do (ii).
The last time a large number of REITs issued new shares was probably the GFC. But that time, the price of the rights share was below the NAV, so effectively, its like an automatic discount, who wouldn't want to buy. But if the price of rights share is above NAV (even if slightly cheaper than market price), I will have to do more due diligence...