There are a lot of great ideas. And a lot of great rifles in this post. However you might want to consider buying one of the Coopers. I believe the model is the Phoenix. You should be able to hit your price point, get the cartridge you want, and have a very fine rifle.
IF not, the $2000 is going to be close without having your action.
I had RHYS build one for me. He has fair pricng and does good work. I would recommend his work. He is a fair guy that will do what he says he will do. That is saying a lot in this day and age.
Below is a picture of the rifle RHYS built for me. It is a HB Varminter in 22-250. And it is a shooter. Tom.
