I think we are in agreement.
There is no general problem with a one-size-fits-all initial action response with a followup refinement once the initial problems are brought under control. Depending on the particular Type's margin between Vmca and the target speed, it may be wise to be conservative and crank in some bank in case one inadvertantly finds oneself back towards Vmca.
Likewise, many folk don't trim OEI initially (me included - other than for a generic rudder trim input) with the intention of doing so once things have been sorted out. The penalty is that the stick and rudder workload increases if you want to do other things at the same time.