Consider several things -
(a) AFM takeoff performance addresses both AEO and OEI, although the latter is the larger interest. Once the initial takeoff is over, the OEI climb becomes the concern.
(b) AEO, the main aim then should be to stay above the OEI calculated profile so that terrain clearance concerns are not a problem in the event of a failure during the initial climb
(c) for AEO in the case of turns, turn radius may/may not be critical on one/both sides of the splay - this should be made clear in the company's published procedures. If both are critical, then maintaining an arbitrarily higher than procedure-presumed speed OR a higher bank angle can compromise the procedure's design and, hence, terrain clearance. If the terrain problem is only on one side (typically the outside splay) then the higher bank angle may be OK but the higher speed not OK. The procedure should provide sufficient information for pilot guidance such that the pilot need only to fly as prescribed to address the basic concerns.
It really is just not on for the wider pilot community to have to second guess whatever it may have been than the procedure designer was thinking at the time ...
(d) in general, I would expect something along the lines of the following to be in vogue, depending on specific Type handling considerations -
(i) prop, AEO, fly the OEI body angle, or a little higher, subject to turn radius considerations.
(ii) jet, AEO, fly the prescribed body angle, which will give a predictable speed somewhat above V2. Generally, V2 is considerably lower than the best climb speed - it becomes a juggling act to pick a middle ground speed which takes advantage of this but doesn't penalise the takeoff by requiring a specific acceleration to achieve an above V2 speed. Typically, jets look to something around V2+10 to V2+20 as a useful target AEO.
Generally, and especially for the higher performance twinjets, maintaining V2 AEO requires too high a body angle for passenger comfort (read panic) and may impose a significant pilot workload in the event of engine failure from the point of establishing the appropriate OEI numbers - it can be very easy to find oneself well below V2 after the pushing, pulling, and swearing has settled down. Far better, perhaps, to be somewhat closer to the OEI body angle when the noise stops ?
(e) Vx/Vy are pertinent to small GA Types but are not typically a driver in heavy aircraft.
Some specific comments -
do not retract flap until turn complete
emphasis is on speed control for radius control and, secondarily, climb gradient considerations
then a higher speed may be specified. If required, this should be in the procedure
it must be in the procedure otherwise the calculated splays can be totally compromised. With turns, both speed and bank angle become critical.