I bought a BR 4 strap , I find it extremely convenient.
my camera now hangs by my side while I walk the dog.
The 100-400 was no problem, I found heavier the lens the nicer it rests by your side. a light lens on the camera (like my efs 55-250) tends to bounce as you walk
No experience with the grip.. but I think there's a reason the ebay grips are under $100 including battery , I'm a pessimist and would save for genuine grip despite ridiculous higher price.