Rerouting a plumbing air vent pipe
In this case, it doesn't look like you need the vent loop at all, and the 6" height requirement is well-covered by the vent stack going clear up to the roof.

If you want to put that loop in, it definitely isn't going to hurt anything. It just doesn't look like you need it.

You could branch off the vent stack above the junction and use a flatter slope to get the pipe over to the point where you take it vertical. The slope you show is steeper than you strictly need it to be.

The important thing with a plumbing vent is that there is an air break downstream from the p-trap to prevent water pressure from siphoning the trap dry, and to prevent sewer gases under pressure from bubbling up through the water in the trap into your living area.

You can just put an up-turned wye coupling in the existing vent stack just above the existing connections, run it through the same path you show in your diagram, and tie back in with a 90° elbow (or a couple of 45° elbows), and cap off that 2" pipe in the wall straight above the connections to the big drain pipe.

Vent loops are for situations like kitchen islands, where there is no air break vent path without using a little ingenuity to create one