In my experience (non-profit CFO), gifts for donors were things like engraved paperweights or bookends...everyone got the same thing, except their name was on it. We used the organization's logo.
I believe that "personalized" refers to the foundation, not the donor, especially since they're looking to replace flowers as the gift. If you can incorporate the hospital name or logo somehow, that would cover the personalized part, but for major donors, I'd strongly advise staying away from 'crafty' items.
Can you get the name/logo on a key fob in the hospital's colors? Everyone has keys and it's something you're used to making. Bump it up a notch and I think you'd be fine. Major donors don't want major gifts, just a small, thoughtful sign of appreciation...and they will remember next year when writing their checks.
You might want to price a few things at award outlets before you agree to take this on yourself. The foundation may just be thinking you'd be a less expensive option and that might not be the case.