I prefer bluntness and boldness, please keep going with it!
If that's what you wanted you should have told me in the beginning.
It might have been better...
Because I'm afraid the (closest to) worst have happened. 
I woke up today by 7 am and I've been fiddling with this since then. Now I really need to go and I may not be able to finish this today (which was our due date).
For the first few hours I was trying to research new topics to get the best result possible there, using AJAX. It didn't work and I decided to move on before timing out.
Then I went back to my first plan and the first thing I thought about doing, which was adding the gallery block anywhere in the page (only place that's possible for a Shop Page is on the footer) and then simply moving it to the banner place. That should be simple enough. And it kind of was, but...
For whatever reason I couldn't find out, I can't make it rendering work as it should!
Right now, if you go to https://kate-bosse-87i3.squarespace.com/shop-footer and manually resize the window, it will be perfect. That's what I had done hours ago, after just a few moments adding a few tricks for doing that. It's not ideal, but it works.
The problem is if you do not resize the window after it's loaded, it will stay as small as it was on the footer. And after hours trying to fix it in every possible way, I couldn't. I just couldn't. 
It's as frustrating as it can be. Such a minor detail, and so close to the end, but what a road block! It's almost like taking the ladder to go upstairs in a tower only to get there with closed windows and no keys. And the keys are nowhere to be found, no matter where you look or how many times you go up and down seeking for them. They might, in fact, not even exist... And the windows might, in fact, be just really good paint on the wall that tricked me really well.
I will try to come up with some idea later on today, if I'm able to get back at time, or in the next days to come.
You see, programming in such complex environments sometimes require a simple idea. Other times experience can help. And I'm good with having ideas and I do have years of experience specifically with this kind of script... But today nothing of that and not even plenty of time was enough. And it might be something impossible to do, squarespace is limited like that, there are things we just can't do. I still can't believe this would be one of those...
(---...---)
And then... Someone did manage to help me finding the answer! Just awesome (after being almost 7 hours on this, maybe 4 just on this minor "key")!
It's there, it's done. It's not as good as the first solution but in the end it looks as simple as you probably expected.
You have to edit the left footer and whatever gallery you set there will be the banner on every page that's on the script configuration (allowedPagesForFooterBanner). So yeah, you have to manually add which pages you want to the script before it will work. And it is just 1 gallery per global setting this way, no way to customize per page, but you can still use the old method.
I hope I'm not missing anything this time. I really gotta go now! 