Duplicate Quote + change Customer zeroes pricing

We use a quote template customer so we can duplicate a long list of products without adding all the lines to a new quote. When we duplicate this ‘template’ quote and switch it to the intended customer, obviously the pricing resets to 0 and we need to enter all of the pricing line by line.
Does anyone have any advice on how we can retain the pricing when switching a quote to a new customer?
We do not maintain Sales Unit Price for products on part maintenance.

Someone suggested a BPM on Customer change, that copied the price to a UD field before the change, then copies that back to the unit price after the change.

A less automated way would be to use copy and Paste Update from the template Quote, to the new one.