You might be able to get it filled in stages. Your pump will evacuate to about 1/15 of atmospheric, which is to stay that it will evacuate 14 parts
out of 15 of whatever gas is there. So instead of fighting counterflows, just get most of the air out and compress the rest with the mercury column.
After that, invert the column and the remaining air will bubble up, but this time through wide tubing in the close end. Now evacuate again and repeat.
Two or three rounds of this should get you enough fill. You should be able to get about 3/4 fill, say, in the first round.
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