An excellent set of tests to help diagnosis, misses.
By turning off the upstairs rads, it should force the water through the downstairs ones, even if the system is 'unbalanced' - so I think we can rule that out, I think.
Can I ask where you are draining water from? - you use the term 'feed pipe', which suggests someone that is NOT the bleed valve that is present at the top of each radiator.
If you have bled water from lower down at your 'feed pipe' you will not remove trapped air/hydrogen (hydrogen being the product of corrosion in the event a system does not have adequate inhibitor). Please answer this point first
If this is the case, I suspect there is no water in the upper parts of your rads.