It is possible.  

Create the copy invoice - I put DELETE in the memo field as a notation because this is oh so ripe for error if you should get distracted.  So you are actually going to delete the "copy" not the original that is linked when all is said and done.  

Email yourself the copy. 

Edit the copy PDF invoice number to match the original in (2) places:

1. Use a PDF edit tool to change the invoice number from the "copy" to the original that is linked to the estimate. 

2.  You will also need to edit the PDF file name to match that of the original invoice number 

Email this version to your customer.  Delete the copy in quickbooks.  In this manner, nothing changes in your system - the estimate/invoice are correct and linked.  The customer gets the correct formatting and because you changed the invoice numbers, it all matches. 

Yes absolutely sucks.  Is time consuming with an extra 5-7 minutes per each invoice!!!!!   And completely prone to error if you forget to delete.. hence the DELETE in the memo field.  I created a custom report on only that and run it once per week to make sure I didn't forget to delete anything.  I've caught one or two here or there... and I'm very diligent, so you must have checks and balances in place to catch these possible errors because they will happen. 

There you go.  This is the work around.  A total nightmare, but I believe it to be worth the effort to keep our business records in order.