With Eznec the source is placed on the antenna by indicating the wire and segment number in the Source Data window. The feed point then shows up on the Antenna View as a O red circle at the point you assigned. I do not understand the technical aspects for how that happens in Eznec however.
I redid my I-10K model on my new PC. I checked the dimensions against the Manual and I find the radiator length is possibly an inch or so short, but I didn't mess with it. The tune was just like I posted earlier with only a fair match. It was close, but I tuned the model anyway, and it goes just like we would the do with a real antenna...I adjusted T1 and T2 and made sure the radials were set right too.
The best SWR I was able to get is 1.5 SWR.
I did the model over Average Earth soil. The first image in the attached PDF file is the main screen and shows this setting under Ground Description among the others.
I checked the trombone currents, but my model does not show a difference in polarity from side to side...like you noted. I also noted that the magnitude of the currents on the trombone matcher are very strong. IMO this may be why the model shows the horizontal responses it does.
I also set the pattern to show horizontal, vertical, and total field values. The pattern for the vertical part is pretty similar to your model. I don't show as much gain as you do however, but I think your model was over very lossy Earth and that would shows us better gain I think.
I added a mast to my model so I could see the currents flowing on the feed line, but I did not add a feed line to the model. The currents on my tabular currents report show to be very low considering I used a the 32' foot feed line = to the length of the mast I used.
I also made a model in Free Space so I could check the Average Gain results, and that is posted as a separate model. It shows to be a very good low value.
