TP1 = 7.7vdc is probably why the hack is in there. Pretty typical for some of these transformers to put out that much voltage. Maybe they where expecting locations to have low line voltage.
Whether or not it makes the LEDs burn depends on the current limiting resistors inside the LED lamp and probably varies somewhat brand to brand and even color to color. In my xp some SMT type where fine, but got warm, but other types of LEDs that stayed on most of the time got so hot they started to melt.
TP2 probably is reading wrong because of no load/filter cap but check the fuse and the 1n4004 diodes. Some multimeters fail to get a reading for whatever reason. Sticking a resistor in series with positive lead helped on one DMM i was fiddling with. When the driver board is connected it should come up to 230v.