Hi thomas P,
I have flown in a P-40N and have spoken with people who operate P-40s of various sorts, including P-40E and M models. None of them have any trouble climbing at 2,500+ fpm at normal weights. Then again, none are being operated at very heavy weights, either. Most are operating just a small bit less than normal weight and none are at max weight, even with a belly tank. You should not be surprised by that since none have actual guns in them except for one very realistic P-40M restoration. And, none of them are limited to 1,000 HP. Most P-40s in combat in the Pacific didn't use only 43" - 43.5" of MAP. Most used 48" - 60" and the AVG used to use 70" - 75" if they needed to do so. Low MAP flight was the norm for training, not for front-line units. I'd think they would take off at normal power and cruise to battle at normal cruise power but, if it came to combat, my bet is they pushed the throttle forward and used what power it could make, without worrying overly much about MAP book maximums.
I don't have nearly as much first hand experience as Greg, but I have spoken to several P-40 pilots, originally when I was a kid as my father was a journalist for Life magazine with a special interest in war veterans in general and WW2 fighter pilots in particular. I was a little quiet kid he had trained to sit still and shut up (often with the help of a model airplane) but I listend to them talk and occasionally got to ask a few questions of my own after they were done with formal interviews and started drinking. Later in life I've talked to the guys flying the warbirds at airshows, especially the P-40s which I had a special interest in. They do apparently push those engines sometimes, more than I expected, though for regular airshow flying I was told low throttle settings were sufficient, partly because they weren't carrying a full load of fuel.
When I was a little kid I didn't know enough to ask about things like manifold pressure, but one consistent story I remember hearing from guys from the 49th FG and the 23rd FG (former AVG) was that once they had figured out how to push the planes they were able to outrun the Japanese fighters and they would run for their lives, gather their wits, and sometimes come back for another shot. One guy was telling my Dad how he was so shit scared in an air battle he swore to himself he'd never get into an airplane again, but once he pulled away and realized he had gotten free and clear, the panic passed, and he started getting angry and went back looking for targets.
Many units seem to have gone through a shakeout process where they learned they could push the engines a bit harder than the manual said. But Shortround pointed out to me a while back, and I believe he is correct - the heavy MAP overboosting was only doable at pretty low altitudes, and not everybody did it. It certainly put the engine at risk. What is true however is that the manual increased the standard boost levels, just like with so many RAF fighters and others around the world - and P-40s were being used with higher boost, both the Allison and the Merlin-engined ones. This isn't always accounted for in the shorthand on these planes (for example that a P-40K had up to 1550 hp at low altitude according to the WEP setting in the manual).
Allison specifically made changes to strengthen the crank case and crank shafts among other things, to make the engines better able to handle the higher boost, but it's also worth pointing out, as it says in the famous Allison memo on the subject, once the the higher-geared Allison engines came out with the P-40M, the very heavy overboosting was likely to be dangerous and was more likely to blow the engine.
I believe most of this should apply to both P-39s and P-40s obviously, and also P-51A (et al), though I don't know as much detail about the combat history of the P-39.