without risking the possibility of the engine expanding the frame there, you could just loosen the bolts up a lot and try it that way, just pure speculation.
I had a similar problem once, unexplained noise and after multiple, multiple, multiple times of trying to find it one time while it was up on a lift I noticed the left lower control arm bolt hole had a shiny part above it (like it had been moving up/down and made bare metal appear) so we pulled the nut off and the lower control arm bolt hole on the frame had become elongated (egg shape), so we found a really big thick washer and welded it on the frame because there was no other fix and the bolt still had enough room for the nut, worked out great and it was never a problem again even at 324k when I sold it.
my point is to check everything in the area, it could be more than just the cross member, which I had that checked on mine as well the typical fix for that is to remove the bolts and lottery them back on there randomly and re-torque.
another thing that will make noises is the sway bar bushings, take off the D bushings grease well inside and put them back on.