There is the letter from the agent in Ireland in the Lincoln Papers in the Library of Congress promising more men for a fee. If you notice immagration fell at the beginning of the war, and it would be natural it did, but in picked up again DURING the war at a time when it would be natural to wait until it was over to make such a move. So, what was the enticement? Also, the Pope spoke out against the war and the numbers drop off the scale to near nothing near the end, for the Irish, not the Germans.
David