Form 1 info is standard so if you are certain of the details you can do it before your stamp arrives.
Your old builder was probably just being safe so he could copy exactly what was on the form 1.
Both ways are acceptable. However, your builder who wanted to see the form 1 first was protecting himself from making a mistake. And it was proof he could then transfer the completed weapon back to you. If you have the engraving done before hand the complete weapon cannot be transferred back to you. It could be in pieces but that opens another can of worms with the BATF.
If it was a kit to begin with and was not a title 1 weapon you would want to wait until form 1 was in hand. If it was title 1 (completed firearm) before you sent it off and the barrel is NOT populated you could do it before.