With only a 5 digit target there is no need to improve on the common mode rejection or input impedance.
I first ran across this problem with the old Siliconix 4.5 digit integrating converter chipset. Their automatic zero cycle did not correct for common mode rejection of the integrated CMOS input buffer, which could have been worse than 72dB when 86dB was needed, and I guess nobody realized in time that this would ruin the accuracy. They released an update which brought out the signals after the input multiplexer so that an external JFET precision operational amplifier could be used. Precision JFET parts were better, but could barely meet the requirements back then. They recommended the Analog Devices AD542 which was about the best available part at the time. These days there are lots of outstanding JFET parts which can handle 6 digits, and 7 digits with grading. The OPA145 series amazes me.
..LD120/121A/122 I would assume.. Great app notes with very details you may find in the Siliconix 1982 databook.. I got 120/121A in my collection (except that I have a working DMM based on that chipset), perhaps it would work 5.5 digits with discrete chips instead of the 122 and a tiny fpga (instead of the 121A).
That is the one. If you check Google carefully enough, you will find that I have twice designed a replacement front end for these chipsets because burning out the input multiplexer is a common failure. I designed a replacement twice because I forgot that I did it the first time.
The LD120 has the terrible integrated CMOS buffer, and the LD122 is the same chip without the integrated CMOS buffer, so that an external JFET precision operational amplifier can be used instead. Tektronix used the AD542 for the buffer, and I have not seen any recommendation from Siliconix, but I assume there was an application note from Siliconix for the LD122 which I never found. The datasheets for the LD120 and LD122 listed the same accuracy, which is a laugh; there is no way the LD120 could have met those specifications with an CMOS buffer uncorrected for common mode rejection.
I currently have a DM501A with the LD120 on my workbench with a bad input multiplexer, and picked up the parts to replace that part, including an OPA140 for the buffer and a DG419 for the input multiplexer. Higher serial number DM501As used the LD122 with an AD542 which is just barely good enough. At some point I would like to have a stack of DM501As for general use. It might be fun to make a little board for fixing LD120/LD122 instruments, but I fear there will not be enough demand to make it worthwhile.
The run-up and run-down design should be more accurate than Intersil's dual-slope design because dielectric absorption produces proportionally less error, but Siliconix did not correct the common mode rejection of the input buffer so was worse overall. HP published even better application notes about the run-up and run-down integrating ADCs, but for a modern design the LTC2400 or similar is better in every way.