Completely off topic.
That looks like a sweet project.
And some people who didn't read the word CAVE in the OP.
I read it fine and I also read that a 0.5 second gun was used. If a 0.5 second gun was used on this traverse I suspect it may have been used to attain a certain level of accuracy. If that is the case a 2' closure is probably unacceptable. If it just happens to be their everyday gun then fine. Perhaps if the OP could give an idea of what the survey is for?
This "misclosure" doesn't interest me much. See me once the thing is put together and the residuals determined. Closures are so 20th century.
It is just as likely that they were using a 0.5" gun because that is their daily driver. But in order to get 0.5" angles out of a 0.5" gun you are going to need to be setting it, and the targets, on concrete pillars. Setting it on common tripods, and over chalk marks, as pictured, says more about the required precision that the choice of instrument.
Traverse adjustments are intended to correct for random error. 2' sounds like more than random error to me. Even with your less then ideal circumstances you should be able to do much better then that. Are you confident in in the coordinates for your start and ending? I would be looking for a blunder or an overlooked systematic error, rather than an adjustment, but running through adjustment procedures might help you find it.
He said "I would like to get it within 0.25' spatially" so we know it isn't expected to be super good.
They have multiple short legs in the traverse, as small as 20 ft. Centering error, even with McMillan precision, can account for much of the 2 ft closure after propagating azimuths through a long traverse. The calculation I showed in my first post supports that based on centering that is better than can be expected here, as probably indicated by the 0.05 ft discrepancies in repeated distance measurements.
The analysis and any adjustment MUST consider probable centering error if it is to be meaningful, and Star*Net can do that easily. He doesn't seem to have (or have used) a program to do least squares. It's too big for the demo mode of Star*Net. Are there other inexpensive options for him to get least squares capability?
Mutli-track prisms, bipod foresites & Backsites, 20 foot legs, you'll accumulate error quick. Star net will help you sort it out, if you provide realistic error estimates.
How many sets were you turning? FWIW, I don't traverse or side tie with a 360 or multi-track.