Al Mundy, I didn't realize you were a new member when I mentioned hijacking the thread. I apologize. I'm sure you just didn't know where to pose your question.
I suggest you open a new thread. People will be glad to help you if they see your question but right now your inquiries aren't seen on the list of threads that begin the Shotgun forum. So unless someone opens this particular thread to address the OP's question, they won't see your questions.
If possible, when you open a new thread, add several pictures of your gun in its present condition, because the guys who frequent this forum love to see pictures (and pictures are actually helpful to them when they are trying to help you). Many forum members now own, or have owned, or are otherwise familiar with Browning A-5's, so you should get some great advice- that is, if members actually see your question and can see pictures of your gun.
But since I bumped into your question on this thread, and I'll tell you what I think: If I was you, I'd just be concerned with the mechanical condition of my gun. I'd forget the re-blue job and would let my A-5 wear its battle scars proudly. I'd just knock off any existing rust spots by oiling and lightly rubbing those spots with the finest steel wool I could find. Thereafter, I'd just keep my gun well-lubricated to prevent further rust. As far as engraving it goes, I'd personally see that as a frill, but it's your gun, your money, and your business, not mine.
You were quoted $177 for fixing the mechanics of your gun. That's not a frill; that's actually important to its operation and your safety, but it may be that you can get enough help from members of this forum to tell you how to cut down that expense, particularly if all that's involved is just changing out springs and parts and such. I'm the least mechanically-inclined guy on the planet, a credit manager by trade (just love to shoot guns), but several kind souls on this forum once walked me through fixing my own 45 revolver free, and that would have cost me an easy $100 if I'd had to pay to get it fixed.
Anyway, welcome to the forum, Al, and good luck!