I'm mostly interested in the dating portion.
The first paper you cited listed 85Kr dating as applying to 100,000 to 1,000,000 years, and noted this is beyond the range of 14C. That lower limit seems pretty high to me. But it isn't going to work for hundreds of years. I think that the last few hundred years stuff is for tracing movement of materials, not dating 'em.
Water and ice
that have been isolated from the atmosphere certainly can be "dated"; the date would be the date of isolation from the atmosphere, not the date of the water molecules. Maybe not widely applicable. However, ice core dating does relay somewhat on 14C dating (that's why ice cores aren't used in the 14C calibration curves) , and this could be an independent way of calibrating them. The samples would be awfully small, far from 16 tons!
The 85Kr dating is fascinating and has obvious parallels to 14C dating. 85Kr is continuously being created. Presumably it's evenly distributed in the atmosphere and dtaeale artifacts are in equilibrium with the atmosphere. When they are isolated form the atmosphere, usually by burial, the 85Kr is no longer replenished and the amount decreases in the usual manner for radioactive decay while the non-radiogenic Kr isotopes just sit there. Measuring the ratio of radiogenic Kr to non-radiogenic Kr in a sample and comparing it to the atmospheric ratio tells you how long it's been isolated from the atmosphere.
It's comparable to Libby's earliest work on 14C. Has the atmospheric ratio been constant over those milennia? Wads the sample really in equilibrium with the atmosphere? What contamination possibilities are there in the ground in in the procurement and measurement processes? There probably are ways to calibrate it against geological dating methods as 14C is calibrated against other dating methods.
It seems to me that the laser is mostly a way of trapping and cooling the atoms. I didn't study the instrumentation description closely yet. But the overall breakthrough in instrumentation is measuring
incredibly small ratios of radiogenic to non-radogenic isotopes of the same element.