Get the BBQ way up over 200C. Shut the lid. Sears and seals the outside of the meat, puts a light crust on. The middle is moist and tender. I will quickly check with a meat temp probe, as soon as I get 60C is good to go for me (some go lower, others to 70C)
I cook them whole, cut them up after cooking. I may marinade for upto 12 hours beforehand, or go for no spice / marinade / rub depending on tastes of guests.
Hot and Quick to sear. If you want it a little better done leave it on indirect heat for a few minutes. The only reason it will dry out is you leave it on too long. Saying that I have smoked a full loin for over 3 hours at less than 90C. It was beautiful but the biggest problem I had was keeping the smoker working at that low temp.
Make sure coals are very hot, put on bbq, drink one glass of wine, turn it over, drink another glass of wine, remove from bbq and serve! If it is dry your coals have not been hot enough and/or too many glasses of wine!
Yes, I agree with #7. If you're concerned about it being overly red in the middle push a metal skewer through the middle (it'll also help manoeuvring it on the heat) and it'll transfer the heat through to the centre. If you think your BBQ is too hot and you have limited adjustment to stop the heat excessively carbonising the meat then get a couple of coke cans (or similar) cut the top and bottom off (should be able to do this with domestic scissors) place them end on on the BQQ, let the paint burn off - typically a nanosecond with a coke can - and rest the loin across the top. It allows adjustment from 25mm to 100mm +. It's saved me on more than one occasion in a high pressure gig.