This thread pops out of the wood work occasionally.. So I read back about 6 or 7 pages to catch up today...
I'll throw my comments into the mix here...
1) regarding the FPGA: I think a low cost iCE40 with 384 LUTS for < $2.00 (qty 1 from digikey) is good enough to time the discharge on the downslope, from top to zero-crossing. Also, the STM32 counters might be fast enough, but not wide enough and will overflow (do you have timings done yet? How long does a cycle last?). Each iCE40 LUT has 1 LUT, 1 FF, and carry logic, so there is enough there for a few 24 bit counters, and you might even have enough to make a voltage and current ADC if you wanted to. Also see my #6 below regarding the need for voltage and current.
2) the comparator needs to have low offset, and reasonably fast propagation time. Presumably less than 1 clock cycle otherwise you are losing counts. If you are counting at 100Mhz (10ns) you need a comparator that can switch it's output in < 10ns. If it's slower, you get count errors.
How fast you need to count depends on your desired resolution, the charge up/charge down times, and how many conversions per second you want to achieve.
3) there is an old trick from the Keithley meters to get higher resolutions without necessarily having to go to really high-speed counters (i.e. 100Mhz) and expensive high-speed comparators and precision op-amps..What they do is, for example, count with 10Mhz, then when the zero-crossing occurs, they take that count and save it. Then they amplify the residual on the integrating capacitor x10, reset the counter, and time the discharge of that amplified amount until the zero-crossing again. When it crosses zero, they add that count (divided by 10) to the previous total, then they take the residual of that, once more, x10 again, reset the counter and discharge that to zero. This gives two more digits of precision, using a slower counter, and less precise comparators. And of course it's slower and takes more time. But maybe it's something you want to consider too, to be able to use less expensive parts and still get good precision. If you do this residual discharge with a 100Mhz clock, you might get extra digits into the 7-1/2 to 8-1/2 regions (assuming that the noise, leakage etc, is well controlled).
4) regarding the input buffer: I think your first choice of LTC6240 is still the best choice. It's < $4 and the chopper stabilized LT1052 is more than $12. Unless I am mistaken, the drift is not important on the input buffer (enlighten me if I am wrong about this). I think the input buffer only has to be stable for 1 conversion cycle. However, for the reference buffer you want to use a chopper stabilized opamp like the LT1052 (maybe not that one for that purpose, just pointing out that the zero-drift is more important on the reference buffer than it is on the input buffer).
5) for the display, there are plenty of 4.7" and 5" 800x400 LCD with touch displays these days. usually between $20-30. That's not too bad and makes a nice user interface possible.
6) finally, I am working on an LCR meter design that uses a 24bit delta sigma ADC ( I am also using the LT6240 as input buffers on that project.. they *are* very nice). You can use the STM32F4 pwm outputs to generate the sine (100Hz, 1kHz, 10Khz, 100Khz, etc), low pass filter it and send it into the device under test. Then measure the voltage across it and current through it and do the calculations. The FPU in the STM32F4 will help here. It's really, really simple to do. I'd be happy to join up on the project and do the LCR part, but the entire AFE has to support 4 wire mode and is basically floating above ground (I measure between RED/BLACK sense leads differentially with two LTC6240s and amplify that with a 3rd difference amplifier, then send it into the ADC). Current through the DUT I measure from the black sense lead through a current sense network returning to analog ground. For a multimeter we'd need to put the voltage divider in front of that. If you want LCR capabilities, you be best to consider it up front.
Sounds like an interesting project,
Cheers!