As stated above, rated charging output is at 4000RPM which is basically highway speeds ... Or low gear around town ... Yes, the battery tender meter will tell the tale ...
I can tell you with certainty that everything that you have done so far is making sense and from where I am sitting it sounds like the bike is operating up to design spec. Either there is an intermittent short or other intermittent drain that we have not seen yet or the lights are the culprit.
As far as the first new battery, did you charge it to 100% before using it ? It could have something to do with the results you saw. Also, it is not necessarily odd for batteries to be bad right out of the box. It is reasonably common ...
Also, are those lights hooked up so that they can be turned on when the bike is not running ? That is the kiss of death from my perspective. That is asking for trouble. High draw items need to be powered via a relay that only allows current flow when the engine is running ...
Also, when you get the battery meter and start riding, the magic number is 12.8 volts. If your charging system is reading lower than 12.8 at the battery terminals, the system is not putting out enough current to supply your accessories AND charge the battery. At this point, the battery will begin to drain to make up the difference. If over 12.8, the system is putting out more power than the accessories are drawing and the battery is absorbing the excess (charging).
Mine usually puts out about 13.3 to 13.5 when I am riding around using my heated gear which draws around 60 watts or so ... I would expect yours to be in this range as well ...
After you get into this, maybe ride around at 2000 or 2500 RPM and power on those lights ... See what that does to the voltage ...
Here is a link to a graph showing the "state of charge" of a battery based on voltage measured at the terminals.
https://www.marxrv.com/12volt/voltchart1.gif
Let us know ...