How good is that known point? Might that be the issue, worth a double check?
While not good enough for boundary work, if this is topo or something requiring less accurate location, wells, wetflags, etc, it's acceptable.
I never used Starnet to 'adjust' data. Fooling yourself into thinking you make the data better is a completely different thread. What it does do is evaluate data by detecting blunders and validating error estimates.
I would spend some time looking for the error before doing any field work over. More often than not a little office time can eliminate return trips to the field.
The more oddly shaped structure to the traverse will create large closure differences at the closing points. While 2' is large, what least squares will show is that a small change to a few angles of 5 or 10 seconds or a distance of a hundredth or two may tighten up the control back to his accuracy limits. I have had odd traverses that the crew comes back thinking they had a major error because the EOC was 0.5'+ but when the adjustment was performed through starnet and the small little problems were tweaked the traverse was actually fairly tight. You're not making the measurements better but you are losing the effects of small error propagation through the network. I go back to these types of odd traverses frequently and have a lot of success doing follow on work that confirms the original adjustment was solid or worst case better than it could have been with another adjustment type.
I'm 100 percent sure its purely angular error since the vertical was flat. I double checked all the distances when I was traversing and had nothing over 0.05' horizontal error.
To use precise language, while the misclosure may be in the direction most affected by angles, the usual suspect in a case of this type are the centering errors. Same with your 0.05' distance error. The distances (from gun to glass) are much better than that. Probably no more than 0.005'. It is the centering of the gun and target over the marks that are causing you to read 0.05' differences. If you are off center as much as that in the direction of the traverse line sometimes, you will be off center perpendicular to the traverse line by as much at other times. A centering error of 0.05' on the early part of the traverse, unadjusted, can easily propagate into a 2' misclosure.
If you haven't done it recently you might check your rod bubbles and tribrachs. But for a traverse through a cave I expect that this thing can be adjusted satisfactorily.