I have that same wheel (T300 Alcantara) and I've been exploring that solution. It can be done easily. The problem is that the space between the base and the wheel is not much and the monitor can obstruct your enthusiastic driving sometimes. Actually I have removed the flappy paddles on my unit just to have more free room there. In real racing cars the dash display is much further away from the steering wheel. The solution would be some way to add extra distance. I think the only available option for that is a quick release + adaptor. Is there any of these on the market that is not terribly expensive and that is easy to install, not requiring electronic abilities and dissasenbling all the wheel? It seems that the quick releases available are made for installing real steering wheels but not for the Thurstmaster wheels. I don't know if I could just add some spacers on the 3 attachments... Finally, another option is to place the screen on the side of the side of the wheel, on a desk mount or something like that. Some real rally drivers have it that way. However, I guess it would not be too practical because it would be a bit out of your sight line.
Testing a possible prototype:
Maybe you can try to put the screen behind the panel, this will give you more room for your hands.
I will receive mine this week and I will try to do something like you did for testing.