< $ 200

         I don't have a good handle on current values but I will chime in regardless.
          The bottom line on any item that is collectible , semi collectible , or just plain something that isn't made currently is that it is worth whatever some person is willing to pay for it.
         I have seen 03 a3s that were in pretty bad shape,barely better than wall hangers being bought and sold for $300+ with both buyer and seller thinking they did ok.
      6 or 8 years back I bought one that had a beautiful barrel ,super smooth action , and decent trigger. It had a horrendous but solid stock and the Rifle had been drilled for an old target scope. (scope not included) this was one scope block on the receiver and one up forward on the barrel. Hand guard that didn't match had a hole chopped for this scope block. Apparently this gun was used for cast bullet matches. I bought it for a shooter and it does shoot wonderful. I paid $275 at the time without the scope.
       It sounds like this gun was set up after WWII for a match rifle, It would be interesting if the old gent has any documentation of his shooting in any matches. It would also be interesting if the old gent would pen a short history of this gun and keep it with the gun along with any paperwork he has .
       Would any of this paperwork add to the value? Maybe not but it would add interest. Now if the rifle had been shot at a known match such as Camp Perry or something we are talking something else all together.
       The obvious answer is that this could be a very interesting gun for a shooter so I have got to believe the bottom of the barrel has got to be $400 or $500 just as a shooter and 2x or 3x that with some kind of documented history.
       More than $200 , the sights are worth at least $80 or $100 used

   The above info on the rifle could move it from merely interesting to more of a very interesting possible collectable.
    At any rate I think it a cool piece .

Sporterized rifles go for almost nothing.

The rule for the masses is "Buy the gun, not the story".

That being said, if your rifle has a story, tell it. Some people like that.

If it still looks like mil-spec but with a few careful accuracy features added and a documented history, it's worth something.

Unfortunatly the value of US mil weapons is based on condition condition and originality. 1950-60's bubba 03/A3 match rifles are fairly common and have zero collectability, they were built by people who couldn't afford a Winchester M70 target or Rem 700/40X. It may be a fine range shooter but it has no real collector value and wouldn't even be usefull as a 1000 yd target rifle today.

The rear sight is worth $ 50, the sling if in nice shape $ 50-75. Doesn't sound like much else is salvageable.

I have to agree with Tangeant. While interesting it is not really desirable.  It is bubba'd to the 9th degree and while it may be a decent shooting gun and the parts have some value as parts, the value of the gun these days is in its original condition.  The reason people did that 40 years ago was that it was a 25 dollar gun.  

Basically you have a 25 dollar rifle with fifty dollar sights and a little bit of gunsmith work.  Adjusted for todays market it is worth a couple hundred dollars.  You can always pay him more for the story or maybe find a guy who likes old homemade match rifles.  

Unless he won the Nationals, shot a Kennedy or had the work done by someone famous it is just an old homemade match rifle.  

Post a pic or two if you have them it may help.

RAF, FWIW - I sold one about four years ago that closely matched the one you describe.  It was superbly modified by someone who knew what they were doing.  Bottom line: I got $425 for it from someone who really liked it.  It was tough to sell and took me quite awhile.

Less than $500. A LOT would depend on overall appearance and the quality of the work. I wouldn't mind having such a rifle IF it shot well. Nor would I be embarrassed taking it to a match. But, I wouldn't convert an original rifle today.