Thank you for sharing this idea with us! I too have a hard time with those screws.
While I seldom hoop my actual fabric, that hooping is vital to a project. I have had some slippage in the past from the hoop becoming dislodged. That is how I came to sewing outside the hoop.
See my blog, The Avid Embroidered, here at Annthegran's terrific site because I will be explaining how to work outside the hoop and most important, why it may work better for your project. Hooping is project sensitive but there is always another way to do things.
Best wishes to you and yours, Pat
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