I'm sorry you can't enter quilts. I have a friend in Eastern Europe who has entered shows in the US (Paducah and Houston). The costs to send her quilts (and they were smaller wall hangings, not a queen size bed quilt) was almost $200.
Maybe if she did it again, she could/would send them to me regular (still trackable) and then I'd send them on to for registration. It's a risk but we haven't lost a package yet that way.
If you're thinking of entering a number of shows, and the timing between them works out well, perhaps you can send it once to a US friend with paperwork (or ask a travelling relative/friend to take it to the US and mail it here), but then it gets returned to the friend, who then forwards it on to the next show with paperwork you've supplied, until the end, and then it gets shipped back to you.
Your work is lovely and would be a pleasure to view in a show setting.
Will you be entereing any of your work in the big show in Ireland next year?