it's all going to depend on how much of any given publication on the p-61 you can read online. The chandelles and following landings are mostly found in pilot stories and pireps and accident reports. The three different types of approved landings, can be found in the Pilots training manual. The ideal as presented in the manual was to take the thirty miles needed to slow down, then to either glide in, or land with power off or power on and dirty. Chandelles were "practiced" it seems by most pilots every day. It is singularly the most reported maneuver throughout all the publications. The hammerhead is a quick and dirty chandelle. it accomplishes the same thing: rapid speed reduction which facilitates landing. The reasons for these more rapid landings were multi-fold. Part of it was bragging rights. Like making a landing on a carrier, setting one of these planes down on a short runway, was not easy and using chandelles, added to the pilots prestige. the second reason was that these planes opperated in contested zones where a mile outside of the airbase was enemy heald, and a slow flying aircraft was little more than target practice for the enemy, so the planes had to make a fast approach, then slow down rapidly to land. This was especially present in the CBI theatre where japanese surrounded the majority of air bases scattered throughout china and burma.
The main problem with publications is that they arent cheap, and usually are quite skimpy though they provide a massive amount of relevant material, though you kind of have to ignore the repetitiveness of some of the data. There are several publishers, but the best source i have found is Amazon, where a quicj search through books for P-61 will unveil a plethora of different books available. Youll find these maneuvers as well as an incredibly rich history of the men who flew them, in there..
As a comparison for the reality these units existed in: When I landed at Camh Ran Bay in 1969, The Viet Cong walked mortars up the runway, trying to hit our plane which was a DC-8. Units stationed on small islands had it a tiny bit better and only had to deal with japanese patrol boats sitting off shore looking for target practice..