If the RNG timer is indeed here to stay, and Yoshi absolutely will not budge, how about it being dependent on how the plot became free?

For example:

Demolition timer: No RNG
Relinquished: RNG

Flippers will only have relocation as a bypass, but honestly, I'd rather see that being taken out so people aren't spending, say the price of a small+paying the individual absurd amounts of gil+price of the plot.