AV, if opening the wall is acceptable (which it apparently is in this case), you can insert plywood between the studs. I'd suggest the following method:

Cut a rectangular opening larger than the bracket's wall plate by a couple of inches, but hopefully smaller than the TV. (You can always open the back side of the wall, if it's phycically do-able (i.e., an interior wall)). Note which way the studs' open sides face.

Cut new pieces of metal stud several inches longer than the height of the opening, one for each stud you expose, to reinforce the studs by sistering. Slide the pieces in the wall vertically, and rotate them so they're back-to-back with the exposed studs.

Use the short, pan-head type of self-drilling steel-stud screws to sister these pieces to the original studs, with the upper ends of the new pieces several inches up inside the wall for strength. Now, you will have stud cavities with open stud channels both left and right.

Lastly, cut two wood 2x4 pieces per cavity just long enough to be able to insert them behind the stud flanges horizontally (a hair under 16"), with the flat faces against the inside of what will be the drywall, and screw them in place through the stud flanges.

The wood will also make re-installing the rectangle of drywall for the wall patching easier. As long as you set these cross-pieces at the appropriate height for the bracket, you can't miss getting lag bolts into the wood. Let me see if I can make a drawing.