A good lab that does this routinely really should not put your embryo at risk. There is probably a 95+% chance that it would survive biopsy and freeze assuming skill and practice in biopsy and freeze using vitrification. I think it's a great idea to do this in your situation. Then you will know what is finally going on.
Another thought is to bank embryos . . . . do about 3-4 rounds of IVF, freeze your 3 day embryos, then when you are ready, thaw and let them grow to 5 day. Biopsy and freeze again. Then you can test a batch of them. This is how CCRM does it, I believe. My clinic was not concerned with thawing my blasts, biopsying them, freezing again, and then thawing at some point.
Good luck, and again . . . I would not trust your current clinic to do this. I would really get to one with a top notch lab.