GEICO THEIR ISURED REARENDED MY CAR AND THEY LOWBALLED ME ON DAMAGES AND REFUSED TO PAY FOR A CAR RENTAL FOR MORE THAN 10 DAYS WOODBURY New York

You are asking for something that not a single insurance company would allow you to do.  No insurance company is going to basically give you a "blank check" to keep a car rental until such time you find the car you want.  Actually they are right in the standard of about 10 days.

So what happens after 2 months?  There would be nothing keeping you from keeping the car 6,9,12,24, or even 36 or more months.  You say oh you won't do that.  Well with zero incentive to get a car on the days you actually make the effort to look for cars you will no doubt find issues with them.  You know things like...too many miles, wrong color, there is scratch on the back bumper, I only have a 2 inch clearance for my head and I need 2.1 inches.

Oh and contrary to your thought, there is NOT a shortage of Used Cars...I can guarantee you as a person who needs extra height there are more than 2 cars you will fit into.  You just have to get off your **s and start looking.

Normally I would tell someone that if they don't like the settlement the insurance company is offering to take the person to court.  However, in your case the moment you mention your request of an perpetual rental the judge would even see that as unreasonable and probably hold that against you.

So to suggest something.  Since they get a much cheaper "corporate" rate on car rentals, perhaps you can ask them that if after the 10 days you don't have a car that they allow you to keep renting the car but you will pay for it at THEIR rate.  They may not but at least this begins to be a little more reasonable.

Your demand to them is unreasonable and riduculous.  If it took you six months to find a car, would you expect them to pay?  Two weeks may be stretching the point - two months is ridiculous.