We are currently at the 60 days left mark, but we don t want to shop too soon. We would like to take advantage of upcoming deals. We will also have to do this with our other car which ends next November.
Generally, the best time to start shopping is 1 month prior to the end date of your lease. The reason is that you make your last payment 1 month prior to the end date, and the lease is completely paid off at that point. So you can return your old car anytime in that last month.
You can shop at any dealer for any brand, although some brands offer a "loyalty" bonus if you stick with the same brand. On the other hand other manufacturers sometimes offer "competitive capture" bonuses.
How about learn from your mistake and buy the car at lease end. Stop throwing your money away.
I would start shopping early, that way you can find out about upcoming promotions, and also be sure of what you want before you spend your money on it or sign a contract.
I'd suggest not leasing.