A 670 is a pretty new crane, you shouldn't see any boom drift in that at all. I left the boom vertical on my 40 ton for 2 weeks while jacking around with my swivel, and it never moved. It's not quite like a excavator.
The easiest way to tell where your problem is: boom up to 50-60 degrees, and pull the two lines off that lead to the boom cylinder. After the initial oil runs out of the lines, look which line keeps running a small stream (and it may only be a little drip). If its coming from the "top" side- which has no holding valve, then the oil is bypassing the piston seals. If its coming out of the "bottom" side, the holding valve side- the holding valve is bad. The holding valve should lock the oil in the bottom side, with no bypassing (crane running or not, that oil should be locked in the bottom side). The holding valve requires pressure from the boom down side, to release it.
There is one other possibility. My Grove tms 300 has seen a lot of years and travel. The boom position in the rest, has worn the barrel of the cylinder. If its cold in the morning, it will not hold itself in that one position, until the oil warms up. If you boom up past horizontal, its fine. Your terex hasn't seen that many years, but it may have had some rough travel, on and off the boat, chained down and rough lowboy travel to wherever you are. It may have a damaged piston or barrel, or holding valve from rough travel. I would see if it drifts in all positions overnight. More than 2-5 degrees overnight would be unacceptable to me on a crane that new. If its drifting that much with no load, its drifting with a load.
For a test, I would find something 30,000- 40,000 lbs, boom out 60-70' of stick (20' radius or so) and pick it up. Hold it 6" off the ground, it should stay there for at least a couple hours without moving more than a inch or so. If it's moving down, and on the ground in 10-15 minutes, you've got problems.