at your service, sir...
that tool is not really suited for the MC1 head set. it's meant for the later MC3 head sets and requires to pound the fork out with a hammer. that's an option on the MC1 fork too (but only if the bearings are shot) but as the steerer tube does not stick out much above the head tube it is tricky and needs an adapter. i dont know if the one in that tool kit will fit properly.
what's the problem with the bearings? play? if they are really new they should not have play yet.
check if the fork is properly pressed into the bearings. it may have come loose and slid down a bit. then the play would not be in the bearings but between steerer tube and bearings. there's a ring/thickening at the upper end of the steerer tube which is the bearing seat. if you remove the MC1 and the rubber cap you should see the upper end of that ring ending just above the bearing. if you see a gap between the bearing and steerer tube the fork is not fully inserted.
you can see the upper bearing seat here
also, below the lower bearing seat there's a groove in which the lip of the lower seal should sit. if that groove is visible below the seal the fork is not inserted properly or slid out a bit. difficult to explain...