Last Update
I was correct in my 1st revue.
Although certainly marginal, I simulated here a version of the original TL061 with a Darlington NPN and the feedback network and made it work with and without your suggested change. This 1977 technology is basically laser trimmed differential N type JFETs nulled for offset slapped on a uA741 with minor changes for thermal stability.
I still suspect TI might have made some changes. We will never know for sure without a task force and date codes. (LoL) back to h/w floor sanding for me. Maybe the others can comment.
Update
After reviewing the TI Rev J datasheet, I agree that your solution is a brilliant one. I suspect some very minor changes in the differential emitter follower circuit may have caused a change in the no load Vout drop above Vee when NSC released this in 1977. It has a laser-trimmed internal bias with ultra low 2 uC/‘C Vio offset-stability BiFET Op Amp.
Much like a uA741 , driving a Darlington from a Darlington even with 100k will depend on very subtle changes. If this was made after 1977 with a TI process on the TL081 rev ? , I agree that the driver voltage is marginal. It would be a matter of if the Darlington was hotter from the oven leakage of heat more than the Op Amp thereby like the diode string thermal sensors drop -2.1 (?) mV/‘C, the differential voltage may be enough to drive Ic= 1uA thru 100k in nanoamperes.
So good on you for coming up with this production problem DIY solution.
Reducing the gain by 50% could be tolerated with minor adjustments of other resistors to balance the SC cut Xtal to within 1’C of it’s df/dT=0 curve minimum. The fixed parallel bias R’s would have been a SOT select-on-test in production to tweak within uV or <1’C error in the oven. This is partly assuming the unknown vintage of your IC, TCXO and probably HP or TEK counter. (Or was it a clone?)
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Bob Widlar in 1967 published an article on the interesting accurate properties Vbe verses temperature.
It took decades later before they became disposable thermometers in hospitals.
I recognize this as a class SC cut TCXO usually in 10MHz in double insulated ovens from Vectron for HP vintage precision counters that sold for about $350 for 1e-11 stability per year. They only needed to have a precise oven temperature where the df/dT=0 so that outside thermal variations attenuated by the insulation would cause zero frequency error.
I see no problems in this design, but a few mistakes/omissions in your schematic.
Base Current is limited by design with 100k into a Darlington (hFE=10k) to protect it.
The 2W 220 resistor will have a maximum of ~ 600 mW if anything in the regulator fails.
the Vin+ is now the negative feedback input with the Darlington’s inverted collector output.
the Vin- port may be biased near >= 1.5V where the 4x diode string are high Z near 1uA to avoid self heating. Yet still give high gain error feedback with 1M with a 1 degree C or so tolerance on the setpoint control.
The Vin- port is pulled up perhaps with a similar high impedance to prebias the diodes and then the larger 1M negative feedback is balances the diode current-voltage level for the desired setpoint.
Conclusion
Without values, I see no problems with the design other than your shorting the Op Amp inputs. Reducing the gain with a Vbe pull down is just another way of reducing the gain that is set by all the other resistors. So something has shifted. (Failed in setpoint or pullup resistor values)