Haha. Bless you for even trying read this entire mess. Much of it from me.?
Let me try ?to boil it down to three bullet points:
1) The rubbish transformer loses 90% of your power on most frequencies. When used on a frequency for which the attached wire is a true half wave it only loses 20% of your power. The SWR however will be acceptable on almost all bands.?
2) A binocular core transformer can only be used on one band for which the antenna is a resonant half wave. On that band however it will lose less than 5% of your power. SWR will only be acceptable on this one band.?
3) A tuner can make any wire have acceptable SWR so long as the wire is at least a half wavelength long. This combination will lose 1 - 5% of power depending upon the quality of the tuner itself.?
For multiband operations only option 3 has performance that I would accept. For single band operations any of the 3 is OK with 2 and 3 preferred.?