Richard: I did a quick look for Parker 16 on a couple sites. Of course there are lots of expensive guns. Something like
this one might be an option for you. The damascus has been blued, but there are good damascus barrel restorers on this site. The gun is also off face, but if you are swapping, that won't be an issue for you. This gun is complete, so you could set the rest of it aside for future re-sale if you decided, or a source of parts for your family gun if ever needed. Something like this can get you started at a "reasonable" cost. You might even be able to negotiate a few dollars to help with your project expenses. You should ask the seller if he can measure the barrel wall thicknesses for you. Sometimes clean and shiny bores have been honed to the point the barrel wall is too thin for safe shooting. From discussions on this forum, if they are at least .024" at their thinnest point, that should be okay for your purposes. You can end up with 0 frame barrels and fore end under $1,000 and then the cost of cleaning up the damascus and fitting the barrels to your frame. If there is extensive fitting required, that will cause you similar issues if you ever decide to reassemble the "parts" gun. Damascus clean up is not necessary just to shoot but it sure looks nice when done.
A word of caution. I found the Parker site a couple years ago in my efforts to do essentially what you are setting out to do. I completely understand why you want to do this. Trouble for me is that I have yet to find the right barrels and any candidate whole guns ended up being cleaned up, repaired and put back in the field and still live here. I fell victim to "Parkeritis" and once it has a grip on you, you just have to give up and see where it takes you. It's been a fun journey.
Cheers,
Jack