Epic/MyChart integration

We have a stand-alone web platform (readysetrecover.com) that helps people prepare for surgery focusing on the non-clinical – holistic and logistic aspects (stress reduction via meditation, sleep etc. as well as things like setting up the house, coordinating help from others etc).

We had a meeting with a hospital, and they liked our solution but said their goal is ‘to provide patient education and communication on a single platform'. They currently use Epic and MyChart. In other words, they don’t like the idea of giving patients another site to visit, possibly with a different login, which is understandable.

We can pass data between our site and the hospital EHR system with IRIS for Health, however, this doesn't really address the user side.

Is there any way to integrate that would solve this issue? What do other sites do to create a more unified experience with an existing patient portal? Is there a way to have our site 'live' within MyChart or at least have a seamless sign in to our site once a patient is in MyChart (for example, they'd click a button in MyChart that would take them to our site, with a 'Return to MyChart' option at the top)? Very open to creative solutions here!