I finally got opamp samples and I tested them as ADS1601 bufers. All of them had negligible offset at 2.5 V (which draws only a small current), but it usually got worse at 1.0 and 4.0 V which drew over 6 mA in my case (but could be as bad as 10 mA). I also tested offset's temperature drift, I measured them at 20 and 80 deg. C. I used Agilent 34401A in the high input impedance (>10 Gohm) mode. All the amps were powered from non-symmetric +5 V, except TLC2272 and TLV2186 which can work with +-5V. The results from the best to worst:
-MCP6072 was the best, despite it's the cheapest of the lot. The initial offset was in 0.02 mV range and worsened only to 0.1 mV at 80 deg.C. It kept such good parameters regardless of current load.
-TLV2186 had slighly higher initial offset (still 0.04 mV range), but was rock stable at higher temperature, the changes were practically indistinguishable with 34401A. Again, it was insensitive to load currents.
-AD8602 was rather disappointing, its offset worsened dramatically with load, it was over 1 mV at 1.0 V and 2 mV at 4.0 V. But like TLV2186, they didn't change with temperature.
-OPA378 has different package (SOT-23), so I tested 2 samples at 4.0 V only. They fared pretty poorly, their initial offsets were 2.1 and 4.7 mV and they worsened to 3.7 and 7.1 mV at 80 deg. C. Obviously, they don't like the load. Originally, I wanted to test the dual version OPA2378 in SO-8, but they're sold out at the moment. I wonder if they'd fare as badly...
-TLC2272 didn't work at 4.0 V (that's why I started this thread in the first place), but the offset was 0.1 mV at 2.5 V and 2.5 mV at 1.0 V. The latter was suprisignly stable with temperature, it worsened only to 2.8 mV at 80 deg. C. Not bad, considering it's not a precision amp.
Of course, there were only 2 samples of each type, so the results are not particularly reliable, but at least I could reject the obviously problematic ones. I plan to buy more MCP6072s from a different vendor to see whether their "win" today was just a fluke.
I also tested stability of all the amps, becuase they have to work with a large capacitive load. But all of them worked fine, there was no overshoot on ringing upon Vref ramp-up. It's because their feedback in figure 42 compensates for the parasitic pole.