How do I connect 2 different back accounts using classes? Both transactions share the same EID, but payments need to come from each classes own bank account?

Hello there, @jgl.

You'll have to create parent and sub accounts so you'll be able to connect two bank accounts. Here's how: 

1. Go to the Gear ⚙ and then Chart of Accounts.
2. Select New to create a new account.
3. In the Account Type ▼ drop-down menu choose an account type.
4. In the Detail Type ▼ dropdown, select the detail type best fits types of transactions you want to track. Learn more about detail types.
5. Give your new account a name. You can use the info under the detail type to add a name that fits.
6. Add a description.
7. Put a checkmark in the  Is sub-account of box and then enter the parent account. If you need help, learn more about parent accounts and subaccounts.
8. Choose when you want to start tracking your finances. In the Balance field, enter the amount in the account, and determine the as of date. Enter today's date if you want to start tracking immediately.
9. When you're done,hit Save and Close.

Then you can connect the two sub accounts in the chart of accounts.

For more detailed instruction, see this article:Add an account to your chart of accounts in QuickBooks Online.

Also, I'm adding this article to know more about Chart of Accounts: Understand the chart of accounts in QuickBooks.

Please get back to me if you need anything els. I'm here to help. Wish you all the best.