It sounds like an issue with the fine tuning of either the 2096 or the NJSP system, or potentially local interference precisely on 860.4625 which fades away and allows good reception on 860.46875.
It is suspected that the 2096 can survive rebanding by programming custom tables in, so unless you've done that for this system then the 2096 being "reband-ready" would not cause your problem.
The 860.4625 channel is pre-reband, so if the system is still using it then it hasn't been rebanded yet or they opted out of rebanding that channel (and it wouldn't be rebanded onto 860.46875).
I have some experience working up custom tables for UHF systems -- 800 is standardized so that hasn't been necessary -- and I have some Trunker data on Troop C. Based on that I worked up a few custom configurations you can try which hopefully will have the scanner tune to 860.46875 instead of 860.4625, but otherwise tune channels the same as it does now. You'll naturally need Win96 or a comparable program to program in the multiple custom configs.
1: Base=851.0125, Offset=0, Step=25.0, ChLo=0, ChHi=377
2: Base=860.46875, Offset=378, Step=6.25, ChLo=378, ChHi=378
3: Base=860.4875, Offset=379, Step=25.0, ChLo=379, ChHi=720
I've prepared the above without having Win96 in front of me, and without being able to experiment with it in a 96 or 2096. I suggest you save your current V-scanner before uploading the above to the scanner, to make restoration simplest. You could also delete the custom configs from Win96 and upload the system again, but loading a V-folder is probably even easier).
Please let me know how it works -- I'm really curious. If it doesn't work, I can play with it over the next few days to see if I can come up with anything else.
Jim