I can give an explanation of what is going on with the setup you have, and why the chainrings seem offset from the cassette. I think that perhaps there is not any problem and you don't need to adjust the chainline.
An older bike with a triple drivetrain will have 73mm BB shell (as you said) and a 135mm rear dropout spacing. Standard chanline was 47.5mm. The M6000 group cranks are designed for the modern MTB 142mm or 148mm rear dropout spacing and runs a wider chainline: 48.8mm or 51.8mm respectively. Shimano specs are here. The FC-M6000-2 model crank has the 48.9mm chainline, the FC-M6000-B2 crank has the 51.8mm chainline. Hopefully you have the former. In that case you're chainline is only 1.3mm wider, and your large ring on the new double crank will actually be closer to the centerline of the frame than the large ring on the old triple crank.
If you have a -B2 model, hopefully you can return it and exchange for the -2 model.
Can't believe I missed this - if you have a 73mm BB shell you should not need the two 2.5mm spacers that come with Shimano mountain BBs. Those are for use with MTB frames that have 68mm shells. Check the BB instructions.