If your goal was to just play old Amiga games, you could have chosen cheaper alternatives, but that is water under the bridge (or over the dam and down the drain).
The PicassoII card will allow you to run Workbench at higher resolutions and more colors on your LCD display, but won't help with 99% of the Amiga games you want to play. I am not familiar with the Arxon Scan Doubler, but it should allow you to display all of the 15kHz display modes doubled to 31kHz so you can see them on your LCD monitor. Both items should work just as well in your A4000T as they did in the A4000 desktop computer. The PicassoII has a pass-through port, so you should be able to feed the scan doubled RGB output into the PicassoII and use a single monitor solution to see all the display modes you want on your Amiga.
Welcome back and enjoy the ride.
