Regarding Perf A & Bureaucratic regulation: You don't get the choice. Once the regulators get involved, you just have to comply. However, their involvement has forced some idiots to fly with fatter margins.
If runway is long enough why not reland rather then continue with unknown perhaps catastrofic problem into the air ( like Concord crew), perhaps into IMC, icing and God knows what else.
You can - that's your choice. But if you are flying an aircraft within its limitations it could mean you are legally in both IMC and icing conditions. So if you have a problem when just airborne, just how will you perform a safe land-ahead manoeuvre?
Would you continue takeoff with unknown huge bang in the back into IMC/icing conditions
Yes - that is what you are paid to do. If you decide not, that's your choice. But don't ask for sympathy or understanding if you foul it up. I would also wish you the very best in stopping lawyers from climbing all over you.
In general, you appear to obsessed with re-landing after a failure. Were you taking a day off when Performance A was started? Have you not read the overviews of certification standards? It is intended that modern aircraft will be safe to operate from the start of their take-off roll until they are stationary after having commenced their takeoff roll. Basically Take-off Performance considers engine failures, wind, runways etc. and make an assumption that you'll either fly or stop. Flying and landing are NOT considered because it's too complicated and I'd also suggest beyond that capability of most people here, excepting yourself of course. If you want to do it that's fine. Fill your boots but don't try to sell it here.