I think I understand what the plan is. I just cant tell how the joists are fixed to the studs or rafters (having a hard time with the perspective). All I can see are the metal plates that, I assume, are just reinforcements. So then I am asking how are they fixed tot their crossmembers? If they are strong enough to support the weight then my next thought is how long of a span is that? If it’s several feet then I would not want to center it on the joists. The final question is “after unstallation, what if someone were to hang on it? Would it still hold?” I’m kinda imagining you’re looking to install a heavy bag.

From the pic it looks like all the weight will be supported by the two 2x4s that you intend to span with the new 2x2 or 4x4. I don’t think the question is which material you should use. The question seems to be “are those four anchor points on the two trusses strong enough to support another 500 lbs?”