Brak...remote deep cycle battery near the thruster is a good idea. Lets say 100ah group 30. Two options:
1.Echo charger which will recharge it after house bank is fully charged.
2. Separate small 3 stage charger of 20amps or less that can be run off your inverter. A bit less efficient but makes a lot of sense in terms of ease of wiring.
Now even a 2kw thruster is gonna draw 167 amps...or about 3amphours per minute of use. Thus a 100ah battery will give you about 15 minutes of use before recharging is required...so sizing your bank to the amps required needs to be considered as well...but 15 minutes is a LOT of use on a thruster. If you need a bigger thruster for your boat...then you start getting into a need for a bigger battery capacity.
I like to keep things simple and minimal. I would probably need thruster for a total of 30 seconds per day if using a slip (to get through the turn that my boat's steering capabilities otherwise won't let me do). And my boat is relatively easy to push so essentially smallest size thruster would do the job just fine. Though maxpower recommends their 6.4hp thruster for boats 30-42' (which could easily require 400 amps)
What are these echo chargers, do you have a link to something I can look at? The description sounds very much like what I am looking for.