That's the route I would go, and upgrade the stock later when you have saved more money. Have the gunsmith rework the factory Remington trigger until you have more $$$ to spend on that as well.
Trued 700 action currently on the EE: $600
barrel: $500
Gunsmith chambering and bedding: $300
Leave you with $350 for the stock and bottom metal, and trigger. $1750 will be tricky, would have to get lucky on the EE.