We just had our basement finished off, with a work out room.   In my prior house, we had what I felt was study ceiling beams/joists made of several 2x4's that I just screwed an eye hook into to mount the TRX.

I did buy the TRX- X-mount for the new house as I wanted two points of contact with the wood as opposed to one big one from another eye hook screw.   The thing is, the "ceiling" of the basement is the Silent Floor style wood joists. As a result, the I beam has a very narrow center part or particle board and the lower part of the i beam is thin in thickness also, so screws of any strength and length will go all the way through it.  The narrowness of the vertical aspect of the i beam will make it hard to mount a decent sized screw into it, and I will have to be very precise, as I have a finished ceiling between myself and the Silent Floor joists.   By pinching the vertical aspect of the wood beams, I would guess that I only have about 1/2 at the most of width of this part of the joist.

I could go into a wall stud, but I am not sure if that will be strong enough.   I am pushing 245+ lbs.

I have the same Silent Floor wood joists, and recently affixed the x-mount. I have had no problems with it (I am 160 lbs). I used the screws with the x-mount, and about half the length cuts into and on the side of the particle board. This is okay, as the particle board doesn't provide structural support. I had some concerns initially, but those were put to rest when my father-in-law, who has built several houses, inspected it.