It is doable. With that sort of budget the boat will be quite small (25-30 feet) and basic. You would have to decide if the comfort/money ratio makes sense for you. It is a long way and, to my mind, it would make sense visit more places along the coast of the Americas on the way (as far as mainland Ecuador).
Check the restrictions for where you can go in Ecuador and how long you want to stay. Considering it is your 'destination' you would want to get more than the standard clearance which gives you a maximum of 20 days in one of two harbors. You can get an 'autografo' which lets you visit 4 or 5 spots over a longer period of time. Takes longer to arrange and costs more.
If your goal is to only visit the Galapagos I would be inclined to look at crewing opportunities, perhaps starting in Panama City or perhaps Mexico. Would be much cheaper and easier - or take an airplane.
Heading back to Lake Ontario for this summer. Ainia is back in North America for the first time since 2010. Currently in Long Island Sound.