Measuring the antenna on an analyser will always need a link from the feed-point via coax as the analyser has a coax socket. (However that short length of coax should not be close to a quarter or half wavelength long otherwise that will affect the readings dramatically).
My RigExpert indicates both the SWR and the impedance and resistive, inductive and capacitive loads that it sees and these change when for example the length of the loop is changed. Whether the coax run is affecting the readings, I don’t think so. I have never however seen in any article that the impedance of a horizontal loop is as low as 50 ohms - I have seen values of 100-250 ohms given. In my case mine measured at (approximately) 150 ohms. Earlier constructions had it down at 100 ohms when it ran in a different layout in the garden. So perhaps, as your model shows, having it a perfect circle at 7m AGL will bring the impedance down to 50 ohms?
I wish I had the room to install the antenna in a perfect circle as that would also give the maximum area within the loop, which equates to maximum gain (or so I have read).
I believe your model is based on a perfect circle of wire? My actual installation is nearer to a triangle shape - just because that’s the only way I can get it in my small garden.
If you are getting 1.08:1 from the antenna without any transforming balun or Q-section that would confirm that you must be close to 50 ohms.
As always there is what should be in theory and then different results in practice - your model also indicates the antenna should be good for NVIS which is not my experience, perhap[s because of how I have the loop run.
I see very little gain on 40m over a dipole but on 20m I would confirm it to be about 1.5 to 2 S-points better than a dipole but almost more important, on all bands my noise level is 1 S-point less than when using a simple dipole.
Everyone I have talked to who has been able to put up a horizontal loop - no matter how constrained in shape - has said they have been surprised by the improved performance over other wire antennas.