Electrical 5/8, nope. Physical 5/8, sure, but only due to luck on the size of the upper vertical element and cap hat. I noticed a fair number of claims from elsewhere (not this site) claiming it was a 5/8, and in some cases trying to show it. I was surprised that that claim wasn't also being made by at least someone here. I was actually almost joking with that statement.
I tend to have faith in my models unless I have reason to believe they are wrong. I would say the high SWR that my model is showing in this case was lower than I would have expected based on the antenna's lay out with no mast.
So basically, we are trying to use feed line to simulate the basket area of the AP? Did I get that part right? That would put the 1/4 wavelength section on the side of the feed point? OK, that gives me something to try and visualize...
As far as this conversation goes, I haven't figured that out yet... 
I wouldn't say that the software can't handle it. I would say the software handles it differently than you seem to think it should, and I gave my thought on why I think the software handles it that way.
The model with the feed point at the same height as the I-10k would put the feed point at about 433 inches in height. The model that puts the tips at the same height would put the feed point at about 638 inches in height. The word "about" is used because one of the models is in meters and the other is in inches, and because of this the models didn't line up to the perfect inch.
I think I should also point out, to be thorough, that the I-10k model I made wasn't specifically made to the I-10k's specs, but was me playing with the "trombone" style of matching system, which I was able to make it work for any number of antenna lengths. It really is a versatile matching system that works with far more than 5/8 wavelength antennas. The antenna I used to compare it to was not actually a full 5/8 wavelengths in length as its tip is at 6.38 meters above the radials instead of 6.875 meters, which is 5/8 for a raw 11 meters. This length was used in that model because with this antenna and trombone matching system fully tuned, this is the length that modeling shows produces the most gain.
The DB