I have doubled and then floated another piece of top. As mentioned above, you need a fairly think WSS (water-solvable stabilizer). The design can become distorted in the hoop with tearing so you are wise to address the issue if it starts.
Here are tips on this site that might help.
https://www.emblibrary.com/EL/ELProj...oductid=PR2105
What is the stitch count of your design? Are you putting multiple designs on one hooping? It might work better to use a smaller hoop size if possible.
Another helpful blog post for you.
https://www.urbanthreads.com/tutoria...estanding+lace
Best wishes on fixing the issues.