If I understand your description correctly, your first method is not for tramming the head it just checks how level you have set your work piece, in this case your parallel. However that method should give you equal results in each direction, the fact that there is a 3 thou difference indicates that you have some slop in the slides or other fault.
Your second method, machining and checking is perfectly valid albeit tedious.
To tram the head to the table surface, using the most common method you need to mount the indicator on your spindle set at a radius just a bit less than the width of the table for checking the Y, you could use the same radius or greater for the X. Then drop your quill or raise the table so that the indicator is touching the table at rt angles to its travel. Set zero or note the indicator reading. Rotate the spindle by approximately 180 deg, being careful not to bash the indicator on the table slots. The table surface will be trammed to the table surface when the two readings are equal. Rather than putting the indicator directly on the table many people use a small spacer on the table and swap it from side to side as you take a reading, a round magnet is common. this makes it easier to not bash the stylus. Adjusting the head can drive you mad because if for example you get a 5 thou error you may expect that rotating the head so that the reading is halved would bring it into line, but it does not. The problem is because the axis that the head rotates about is much higher than the line between the two measuring points, resulting in a large horizontal component in the gauge movement.
To make tramming easier you can buy or make a holder for two indicators. You set one to zero at a certain position on the table, a round magnet is a good idea, then you rotate the spindle and zero the second gauge at the same point (magnet). Now all you have to do is lower the quill or raise the table until both gauges are deflected a small amount, the head is trammed when both read the same. You then rotate the spindle 90 deg to check tramming on the other axis if your head is adjustable on both axis.
I mentioned that this trams the head to the table surface, but what if the table surface is not true to the table motion? For normal machining I use the double dial method described above because it is quick and pretty accurate. When I need the maximum possible accuracy I use another method to tram to the table motion. My fly cutter is full circle and quite large in diameter (http://www.homemadetools.net/forum/d...995#post100445), I put a round magnet on the bottom surface near the outside. Then I set the spindle so that the magnet to spindle axis line is in rough alignment to the travel direction. I mount an indicator on the table pointing upward which I align under the magnet and drop the quill to place the magnet on the dial stylus and zero the reading. The I rotate the spindle 180 deg and move the table to place the stylus on the magnet again. If it reads zero then the spindle is trammed to the table motion. This is easier and quicker than this description might indicate.

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