Based on your most recent information, the head-to-column interface at the dovetail ways is sloppy and needs to be corrected before any of the other tests and tramming processes are appropriate. Sounds like some combination of gib fit, rough or wavy way surfaces on either the head mounting or the column, or both.
On my Rong Fu 45 (Taiwan manufacture), with a properly fitted and adjusted gib, the head would sag no more than 0.003” when the locking levers were loosened (often less), yet the head would move up/down (with levers unlocked) without excessive force. Loosening the gib would not significantly ease the force required to raise/lower the head, but did induce more head sag, but did not alter the tilt or lateral position. Granted, I hand fitted the gib to the dovetails using Prussian Blue marking and Swiss files/lapping with 500 grit paper on glass. But even before that fitting, the sag was no where near what you are experiencing (0.008” as I recall).
I recommend you get a replacement gib, then re-test and be prepared to tweak the gib fit (common need with entry level Chinese equipment), or exchange the mill for a replacement. A badly fitting gib can be the source of the head wallowing around under pressure or relocation on the column even when it’s clamped down to a point the head won’t move.