Like you, I could not work on quilts loaded with dog or cat hair. Are the quilts you are getting also starched? That doesn't help me with allergies.
The only suggestion I can make is to ask the QOV folks to have their quilt makers put a note on the quilt tops they make when they are donated. The note should simply specify "from a pet free home" or "Pets in home of maker".
Someone suggested that the quilt tops be tossed in the dryer with a damp towel to remove the pet hair and dander. I don't know if that would work, but it would reduce the problem. I use this method to remove loose threads that my quilts attract when I'm not looking.
As for justifying your long arm - you don't have to justify your long arm. If it gives you pleasure to use it, that's justification enough.