aircraft,

In the olden days to which you refer, the OEMs didn't use the GAMA POH with its expansive text.

Vx is fine, if the aircraft is capable of climbing at that speed, the weather conditions are reasonable, the general terrain is benign, and the preflight sums have been done. Very difficult to generalise with Vx .. as it is with Vy. At some stage, however, in the continued takeoff, one needs to clean up and get to the cruise-climb environment. There is no easy answer .. which is why a lot of us prefer to abort if that is anything like a feasible option....

Consider that the POH words are there to meet regulatory and Industry convention requirements and protect the OEM to the maximum extent feasible ...

As much has to be read into the POH words between the lines as is read literally and, generally, the Industry pilot just doesn't have the background to read too far beyond the literal words.

Looking at some of the specific words you cite, it all depends ... for most twins at a decent weight, Vx is not all that relevant as the climb might well be negative ... after one cleans up (at whatever stage), one might be better off with around 2-3 degrees bank, primary controls rather than trim (provided one's manipulative skills were OK)

The POH intent is to control first with the primary controls and then trim when duties and workload permit .. certainly NOT an immediate priority .. depending on skill and currency levels, of course.

As you observe, "obstacle" is anything into which one might blunder ... even a gently sloping incline. The big problem, as I see it, is that much training is done at light weights and pilots get an unrealistic idea of what the beast might do when one quits. As for eyeballing obstacles, that is just plain imagination ... either one does the sums or one throws the dice on the day.

Turning flight involves a reduction in climb gradient ... no argument there ... it comes down to a case of which is better ... a straight flight path to higher obstacles or a turn, lose a bit of height, and head toward benign terrain ... again, something to be preplanned, not cobbled together during the escape procedure.

However, it is important that these issues be canvassed in a forum such as this so that different points of view can be argued. At day's end, it comes down to three things ..

(a) did we manage to get to a safe height and see a satisfactory conclusion to the flight ? If so, then a sigh of relief.

(b) if we aborted, did we walk away and can we argue the decision process in court ?

(c) if we continue and come to grief (hopefully walking away), can we argue the decision process and the flight management in court ?

Anyone who thinks that the arguing in court bit is not important should discuss the subject with some who have had to do just that. And, if you lose, it can be VERY expensive.