"The primary line from the boiler goes through the heat exchanger, then the heating loop in the DHW tank before returning to the boiler"
I don't think this is correct?
Your solution #2 seems good.
Sounds like heat exchanger is undersized or under-pumped.
Get a low-cost IR themometer, put 2 wraps of masking tape, 1" wide around pipes so the emissivity will allow IR measurment & check all 4 port temps.
Bare metal won't read correctly.
Side-A is input from boiler, side-B is system.
Mine measures 15-20* delta-T on both A & B sides.
Get a new heating pro.