If anyone decided to re-core an factory radiator, you must know and review your replacement core options and specs with the radiator shop. Who makes the core? 3-row or 4-row of what size tubes? Then the cost options can be wisely reviewed with the purchase of a new radiator.
I believe the OEM radiator core was 3 rows of 3/8" tubes. Pictured below is a 3-row replacement core using 1/2" tubes sold by Detroit Radiator. And a pic of what the original coolers look like inside the end tank. Pics are from Ebay, Sep 2016 for a restored radiator using original end tanks with this new core.
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I don't know what size tubes a 4-row core contains. there are many choices regarding cores - from tubing size to who makes it and where it comes from. All TBD with local radiator shop. The OP does not identify where the leak is.
As was already said, for a stock, 20K mi car, I would conclude the OP would like to retain the originality of the car. So with all that has been said in these posts, compare the cost of repairing or re-coring the original radiator to that of a replacement. The factory radiator worked fine at stock or near stock performance levels, say when stock stuff is maxed out at 360bhp.
As far as core design goes, TType6 above is correct when considering the conductive, convective and radiation heat transfer in consideration of thermal efficiency.
1 row of 2 inch tubes = 2 inches, the optimal design.
2 rows of 1 inch tubes = 2 inches
3 rows of 1/2 inch tubes = 1.5 inch equivalent tube.
3 rows of 3/8 inch tubes = 1 1/8 inch equivalent tube.
the factory core is thinner than the end tanks. if re-coring, it would be ideal to find a core that would be as wide as the end tanks to get the best efficiency possible - tube size TBD. And when using distilled water with coolant, there would not be the mineral calcium buildup restricting flow.
Again, the factory core was fine when new and operating at stock or near stock performance levels.