I had already typed up an answer to your question just before you discovered the discrepancy between the two +10V points.
Obviously informational at this point...
...
How to distinguish a problem in the 10V ref loads and bypasses vs at the 10V Ref power ckt?
...
The usual method is to isloate (unplug) the power supply outputs, put them under load, and measure them. For this unit it's described in the "Regulator Troubleshooting Procedure" (pdf page 474). Since you only care about the +10V ref, you might be able to get away without loading the other outputs.
The +10V ref is driven by an LM324 (see schematic #10), so it doesn't supply much current and is short circuit protected (max current is 60mA). One thing you could try is to connect an external power supply to the +10V reference as-is, set the current limit to say 100mA, and try to supply the reference yourself. This isn't 100% though, since you might end up masking the problem or fighting with an issue in the output stage of the LM324.
If it turns out not to be the supply, finding an intermittent short in a bunch of parallel connected components can be difficult. It involves isolating branches of the suspect circuit. For the first foray, this would be disconnecting the various connectors where the +10V ref flows to at least get it down to the board.
Another approach is to use one of these PCB current probes:
http://www.aimtti.com/product-category/current-probes/aim-i-prober-520It's an investment if you want to expand your collection. Another option is the old HP 547A current tracer probe.
Thermal cameras can sometimes find a short, but in this case we're talking about a small amount of power which wouldn't generate much heat.
Then there's always the shotgun approach of starting with the most likely failures (like those tantalums you mentioned), and start removing them until you find it. More drastic measures can also include cutting traces and lifting component legs.