Yep, the 2x Barlow will turn your 1200mm focal length f/4.72 into a 2400mm f/9.4 scope. A 4x Barlow would get you to f/19 with the 224MC, but they are hard to find and expensive. Maybe a cheaper 5x with the 224 would be OK, or a 3x with the 290? Difficult choice, and not good for a full disc moon, only the DSLR would give you that. However, you can take multiple close-ups and mosaic them together using Microsoft ICE (Image Composite Editor), but that would be a lot of shots.
Having said all that, you can always try the 2X Barlow and planetary camera and see what you get, the planets will be smaller than optimal, but you'll still get a reasonable view.
I tend to use this tool for determine image size, probably better than the Bintel tool.
https://www.12dstring.me.uk/fovcalc.php
Andrew