If you are happy with the push to's go for a 16" Lightbridge. Maximum aperture and Bintel have them priced under your 3k with enough left over for some accessories, like a shroud.
If you want go to you could look at an LX90 or LX200 but you would be down to 8" of aperture to get in under your budget. Half the aperture and I would think something like 75% less light gathering ability of the 16".
Of course you will be posting your 12" dob for sale on here so don't forget to add the proceeds from that to your spending budget

. Should get you some very nice eyepieces or even an Argo Navis for your 16", or even get you closer to a 10" LX90.
I have been contemplating this question with a similar budget in mind for a few months now, but have held off as the weather in Sydney has been garbage unless you want to photograph cloud.
Good luck with your decision.
Wayne