Once I had a tire that didn't want to seat.
After a similar moment of despair, I did put a strap along the circumference.
To squeeze the tire against the rim. But not too much as it needs to inflate.
Then some soapy water, and moving a bit the tire where the air was going out.
And don't worry about the sealant initially, or you'll get it everywhere.
You can deflate a seated tire, and put the sealant trough the valve.
And one last trick.
If you remove the valve's stem core, it allows a higher airflow into the tire.
Once it pops. Place the core back, and re-inflate.