The classic had what was referred to by some in the engineering community as a "postage stamp" windmill inflight start envelope because it was so small. The envelope tops out at 24,000 feet because that was all that was successfully demonstrated. It wasn't because the airplane couldn't hold that altitude. The accepted test technique when you are at altitudes above the point where one engine can hold altitude is to descend through the target altitude at the target speed and initiate the start attempt at approximately the target altitude. Boeing would have preferred to have a 28k or 30k capability, but the engine couldn't windmill start there. At the altitudes where it could windmill start, it required an airspeed (and corresponding windmilling conditions) of I think 300 knots, which was well above the best glide slope speed.
The NG could accomplish stabilized windmill starts at quite a bit lower speed - 260 knots IAS I think it was - much closer to the all engine out best glide slope speed. It still was not a consistent starter above 24,000 feet.
Regarding use of the engines beyond rated thrust, Boeing was just telling crews the conditions under which additional thrust beyond max rated thrust for the airplane model may be available, and advising them to use it as a last resort.
Just in case some non-NG pilots aren't aware, the NGs that are purchased with engines rated lower than the maximum approved rating for the airplane model (700, 800, etc) have the ability to access the maximum rated thrust for that model in an emergency by pushing the levers to the stop in the normal EEC mode as well. (This is the "maximum thrust" feature mentioned in a post above.) As far as I know that is unique to the 737NGs (and maybe Max?) among Boeing models.