There's ways to adjust the angle the camera dangles in, regardless of it's strap lug's locations... I've only recently started playing with this, with my Sony body, since on M4/3 my largest/heaviest lens is the 100-300 II but I don't use it too much and the next largest would've been the PL8-18 or 17/1.2 (the 35-100 would be in the running too since it's longer tho slimmer and about as heavy).
A lot of people seem to like using a strap mounting location near the bottom of the camera (usually on an L plate or ARCA plate, bottom right works better for these purposes) for one end of the strap, while still using the left hand lug for the other end of the strap. I've been doing that a bit now that I got a new plate that makes it easier and with longer lenses it does force them to point down pretty naturally when wearing the strap cross-body as you do.
So now I keep 3x Peak Design Anchors on that body, one on each lug (for when using smaller lenses that easily point forward and are unobtrusive like that), and a third on the bottom right corner where my current plate (by STC Optics) has a full strap lug for precisely this purpose.
I guess the extra dangling bit can look a bit odd to some, but I still prefer this (combined with a strap I can quickly cinch in or loosen up on the fly) over the Black Rapid style where the body glides loosely on the strap by a single attachment point. YMMV, I often switch over to a wrist strap if I'm gonna be putting a larger lens+ body away into the bag often, it's nice to have options.
Edit: The PD plate that comes with some of their straps (for the sole purpose of this, no ARCA dovetails or anything) is as minimal as it gets, it's basically just adding two lugs at the bottom... 'Course you then need to take it off for actual tripod use.
An ultra low-profile connection point for Peak Design Anchors and OEM camera neck straps and wrist straps.
www.peakdesign.com
I've always liked having an L plate on my mid-sized bodies so I could easily do vertical panos or just portrait shots in general without relying on the ballhead's drop slot, so using an L plate with some extra strap mounting options just came natural. Before my current one I had a pretty small Ellie from Three Legged Thing, still got the short version on my E-M5 III, before that I had a RRS on my E-M5 II cause the display presented some extra challenges and that body did benefit from having more of a grip.
I do tend to go for slimmer than average plates, can't stand something that ends up adding close to an inch of thickness all along the body's bottom. They come in pretty handy with mini/tabletop tripods too, where the drop slot + a large lens is precarious.