I'm not sure 1 litre of oil over 5,000 miles is that extreme for these engines. And I've never heard of putting 10w60 oil in. Although the exact recommendation will depend on where on the planet you are. But I believe you are UK?
Oil questions like this on the forum tend to lead back to asking the experts at Opie Oils. @oilman is their forum account.
Also worth a quick look at this.
https://zroadster.org/threads/which-oil-for-3-0-engine.22826/#post-386414
To be honest 1ltr over 5000 miles is pretty good, some people use 1ltr ever 800-1000 miles and that is considered acceptable by BMW. No need to go to the 10w-60, this was used in some M engine but too thick for the 3.0. All it is going to do is rob power, just to pump it around and cause extra heat and friction. Stick with the 5w-30My engineer recommended to change the oil from 5w30 to 10w60 Castrol edge as I had to refill about 1 liter of oil after 5000 miles.
I would need some opinion on this if possible! Thanks in advance!