Additional Work On Your A-5
Really, only you can make that call. In absolute terms, investing that kind of money into the gun would make me pause. Can you find a better value in a similar shotgun in better condition?
If your gun is rare or special, re-bluing will reduce its value. Modern engraving probably won't add value to the gun, unless the engraver is known or will be signing the work.
Search on Gunbroker.com to see how similar guns are being priced. As an example, a friend has a 16 gauge A-5 made by Remington during the WWII era. The gun is pristine and has the steel shot effect on top of the receiver. Beautiful gun, shoots like a charm. He estimates that the gun is worth $700.
If you like to buy and sell guns, you will probably not get your money back out of the gun. If you like to shoot and tend to keep your guns, if the money makes you happy, then take the plunge.