Combining multiple Cones into one cone

Try using single points (autovector points) instead. I used to have problems with auto/measured cones for some reason switched to just points & constructed cones or sets from that. Maybe that was some odd version of pc dmis but I can no longer recall. But I went with points from that point on regardless of what version I work with. Verify your alignment too because stuff like profile and/or position do get affected by crappy alignments or dirty pieces.

So your angles could have more +/- tolerance independently than the profile tolerance condones? Your position would only be the centroid of the feature(s) compared to the datum structure which can pass too depending on the applied tolerance. It seems your detail points are drifting outside your profile tolerance. You can review if it is something consistent by reporting with T-Value for each point instead of attempting to evaluate the set as a whole, then you know where to focus with any correction(s).

Older version of PcDmis:
Construct a cone BFRE.
Select the four pieces and hope the math works since it is using four centroids.
After each one, add .hits[1..conX.numhits] where conX is the name of the feature you are typing that after.

IF the math doesn't work, select things until it does work.
Then add the .hits statement above and delete the features that should not have been included in the first place but you needed to get successful math.

Newer version of PcDmis:
Construct BFRE
select the cones in the window
In the graphics window click the points individually and it will use the points for you.

You are rotating the head, so you want to recomp (the RE part of BFRE).

I've done this with speherical bearing races and dovetail grooves (like you're doing) without issue in the past.

You want to have points that have a common Z, so you have circles of points.
If you have a newer version where you can click the points in the graphic window, click them in circles instead of clicking them by cone segment.

So I think this is giving me the closest to the true result I was expecting. Thank you for your input!

How would I use T-Values to understand whats going on?

NullTie, T-values are localized profile evaluations for individual points. It can help you to see where the stock condition is causing your profile failure. Some people utilize graphs too when looking along an entire surface to understand where the data is going 'bad'.