Problem(s) Encountered:

The dome and the telescope were not synchronized as I was changing positions to targets. I believe the problem was the TCS so I opened it again but I still have the same issue and the telescope reaches its approaching limits. 

Solution:

I was able to stow the telescope from home without issue prior to arriving on the mountain.  The observer was then able to manually home the dome and close it. Once on the mountain, I tried moving the telescope, controlling it via JSkyCalc.  I was surprised when I entered coordinates for a target roughly 2 hours east of zenith to see an HA value of 8 hours register for the target in the TCS “next object” window.  I tried a couple more targets but the same issue persisted.  I also noticed that there were three instances of MaximDL open.  I decided to close all processes on the TCS PC, as well as JSkyCalc.  I reboot the TCS PC and brought all systems back up.  I then reinitialized the tcs terminal window on the workstation (tcinit, tcstatus) and restarted JSkyCalc.  Target coordinates become more realistic after this.  I moved to numerous targets, with the dome slaved to telescope position.  No issues.  Dome was stowed through the TCS, as was the telescope.  No issues.  Finally, I ran a “startup” in Prospero to make sure it was still connected to the tcs,Not sure how target values got so far off.  I did notice that TheSky software on the TCS PC was also open.  Perhaps something in there was inadvertently set in a manner that caused the issue?

From Thorstensen:  It's also possible that JSkyCalc had stopped updating.  One can try "stop update" and "resume update" to see if it behaves,
and if not simply stop it and restart.