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I have another way on how you can use the same template with your new QuickBooks Online company subscription, rtunnell-txreic.
For now, you'll have to export the invoice to Excel and import it again to the other QBO account.
Here's how to export:
Once done, you can import the invoice template to your other account.
For your reference, you might encounter some issues when importing data. Here's an article that you can check out: Common Questions About Importing Data To QuickBooks Online.
Keeps me posted if there's any help you need with the import. I'll be here to assist you anytime you need.