I'm just interested in what somebody who obviously knows what he's doing thinks about that design
Well, in that case I'm not your guy.
But also I still feel there is no real point to the dual band antenna this way since it still uses two separate feeds. Like if you only had one coax to hook up to you SA then fine, but if you have to have two separate connections you might as well ducttape the two tubes together and then have two properly tuned antennas instead of one that's kinda crappy at both bands.
Tuning these is not trivial. A single simulation run takes 15+ minutes on my potato computer, exponentially more if I up the accuracy and then there are 4-5 dimensions that can change to sweep over.
I'm sorry, I don't mean to complain. I offered to simulate these as I am interested too, I'm just trying to explain why is it not easy to do anything else then a single, precisely dimensioned drawing. Being able to tell whether a very particular configuration is good is still somewhat tedious, but to come up with "something like that" just better is an iterative time sync even with proper tools.
At least you can snip the feed wire in real life and see the result immediately on the analyzer. I wish the simulator could do that.
I'll have more time over the weekend I'll play around tho.
Can you post the dimensions of your build as is now? We could start from trying to get a match on the S11 plot between your VNA reading and the sim and work from there on.