Wow, a lot to be responsible for... Fortunatately I have very little need to impress anyone here, because really, what does it matter anyway? I just try to offer a tiny bit of experience, which people may adopt as wisdom if they choose...
"non-standard" and "non-approved" have less meaning in the world of general aviation than they do for large aircraft. Indeed, I'm not sure that "standard" has much regulatory use at all in this realm. As for "approved", the regulatory authorities will generally decline "approving" procedures which differ from those required to show compliance with the requirements applicable to that particular aircraft design. Thus, there are many things which are have no status as "approved", only because nobody sought to approve them, because there was no need at the time. That simple fact does not make them unsafe or prohibited. If, during certification, a certain condition was found to be unsafe, yet did not cause a finding of non compliance with the design requirements, it would be "prohibited", thus obviously "non-approved". Spins being a good example. In some aircraft they are expressed as "Approved", in other aircraft, they are "Not Approved", and yet other aircraft they are "Prohibited". The same aircraft could have two of these conditions, depending upon configuration. So, are you legally permitted to spin an aircraft for which spins are stated as "Not Approved"?
Where the flight manual and placards are silent, air regulations otherwise do not prohibit, and it is not plainly unsafe, it is not forbidden to do it. Pilot's training and judgement must be applied. If training and judgement inadequate, get more!
My choosing to takeoff with less than full power on occasion, when conditions are favourable, is to, in other words, "reinforce my actions" for planning to fly the aircraft in unusual circumstances. It is very certainly my preference, to be safe, to set the power at the time of takeoff rather than as becoming airborne - that is the time a change in power could cause an unexpected loss of power, perhaps more than one sought! By the time I reach the altitude at which I would normally consider it safe to start reducing power, I'm already about the completion altitude for my self appointed excersise.
Reduced power practice on the water is as harmless as step taxiing. If the pilot's technique is such that consistanly good takeoffs are made with less than full power on the water (finding and feeling the step with more awareness) full power takeoffs will be accomplished with greater skill. You can force a waterborne aircraft into the air with power, or you can fly it off with power, and much less strain on the engine. You cannot force it off with reduced power. Therefore, if you got off the water with reduced power, obviously your technique was good, and that was the best way. If I have to check myself out in a floatplane or flying boat I have not flown before, I might do this if I have time.
Yes, if I can detect an engine problem, and abort, I would much rather have the sick engine on the ground. It's not always an option. Several times I have had engines turn sick just as I crossed the trees. If you manage the plane properly, and get it back around safely, the engine will be back on the ground, where it should be, for maintenance. If you forget to fly the sick airplane, you'll be in the trees. There are many reports of crashes after a partial power loss, where it is agreed that plan could have been flown to a safe landing.
I differ, in that I firmly believe that non-standard operations are justified, and indeed, vitally important when conducted safely with preplanning, and not in conflict with flight manual, or other regulatory material. In some cases, formal approval is appropriate. For those pilots who can imagine a non standard operation, which they know they have not training for, they can seek out the training. For operators who can imagine using the aircraft for a task which could require modifications, and might involve degraded performance, formal approval must be sought.
Is towing a glider a standard operation? You're sure flying the aircraft with effectively less than full power! Is flying with a draggy external load, which really affects the performance of the aircraft a standard operation? It can have the effect of reducing performance like having less power. I have approved both such types of operations as only two examples where an aircraft will be flying with less gusto than the "normal" version of that aircraft.
As a personal "check and balance" I like to practice out of the ordinary. It broadens the mind. When I test further out of the ordinary, I apply for a flight permit, that extra check and balance for safety.
Flight permit not required for a partial power takeoff in a 150...
Pilot DAR