I had to look for a bit what actually determines the power supply voltage for the LM10, as there is no other (fixed) voltage regulator, but it's pretty simple. R10 provides some base current for the triple darlington Q5, Q4, Q3, and then a bit more is added for the voltage over the current shunt.
With an extra diode between R10 and Q5 you can give the LM10 a bit more headroom, but at the expense of reducing the maximum output voltage a bit. You could fix that by modifying the triple darlington into a Sziklai configuration, but that may modify the regulation behavior, and thus need quite extensive testing.
Edit, Oops I missed the wire directly above Q2, which forms a direct connection between A2 and the darlington...
The current limit is built around A2, which opens Q2 to starve the darlington of base current. A saturated BJT has a pretty low Collector - Emitter voltage. It may just be possible to add a LED at the collector of Q2. Another quick option is to use an opto coupler. IR leds in optocouplers have a lower voltage drop. Around 900mV and that may give you the headroom you need. The other side of the optocoupler can then drive your LED. A red led in the place of D2 probably does not work because the B-E junction of Q2 also has some 600mV, but an IR led instead of D2 may work.