Monthly car parking in Setagaya-ku

First time buying a car here and trying to figure out the parking situation. I need to buy a car for various reasons asap. I will not have my own parking spot for another 4 months. So I need to find a parking lot for the time being to park my car. I've heard I'm limited to a 2km radius from my apartment. Is that correct and if so are there any possible exceptions/workarounds? Like parking in hourly rate car parks or get some kind of permission to park somewhere else in Tokyo temporarily? I am using websites like parking navi and park direct and there is nothing available near my place.

by muku_