Katie, what color were the flowers you tried pressing? I'm wondering if a darker colored flower might work better for that purpose? I've never tried preserving hippeastrum flowers, I've only dried much smaller blooms.

The first attempt was with a darker pink double flowering one. I tried both pressing the entire flower, which was too big and started to rot, then tried just pressing the individual petals and they melted away basically. I've had mixed success with pressing lilies so I was hoping to be able to do the same with my hippeas.

Hippeastrum flower tissue seems to have a very high water content which might predispose them to major shrinkage and/or rot while drying. Perhaps you could try using a dehydrator or some other method to minimize the drying time? Maybe that would preserve more of the original flower structure.