Your agent is correct. Pay for remaining excess and send for reimbursement is the correct way.

Different policy, different insurance have different coverage, and different assessment. You cannot expect other insurer to 100% cover all the remaining excess.

Don't even think about splitting the hospital bill because it will complicate things - some thing in the bill will raises some questions, some inconsistencies because the billing people did a sloppy job that will further delay your final GL.

Alternatively, why not just request GL under your personal insurance?

Technically, I don't think there's anything in the policy wording saying against doing this, so I think it should be okay.

You do have to provide all the complete documents tho.

Go to billing counter. Request for full itemized bill, all medical report and all lab reports. Say for insurance claim purpose. They should have it in pdf. Have them emailed.