Persistent storage in captive portals or mobile internet while wifi connection without internet

I have a little problem here:
I want to create a WiFi network, which does not provide internet access. The WiFi network should only serve one website to the user like in a museum.
That's pretty simple right? But here comes the hard part:
I need to store persistent cookies (to save the user's answers and display them back later to the user) AND the mobile internet connection should NOT be interrupted (because the WiFi does not offer an internet connection). Why is this a problem?
I you connect to a WiFi with a mobile device, regardless if you have internet access or not, the mobile connection will be cut. There is only one exception: The internet is blocked (or at least seems blocked) by a captive portal. But if you use the captive portal "browser" you can not store persistent cookies. If the "browser" is closed, all is lost.
So how can I solve that? Sure, the user can use the "normal" browser, but as far as I know this is not possible on iOS. If you open Safari, the "captive portal browser" is raised over Safari...

Would be great, if there is a way to do that......

EDIT: The config files can all be found here: https://pastebin.com/kYzPw6C4
To clarify: The clients can connect and the captive portal opens, but I need persistent cookies. And that is not possible in the "captive portal browser". But without the captive portal the client devices cut the mobile connection even if there is no internet connection via my WiFi....

Cookies persisting after captive portal pages will not be allowed. Apple closed an iOS security flaw where malicious captive portals stole auth cookies. Wireless Broadband Alliance acknowledges that most devices will not save cookies from the captive portal mini browser.

Maybe allow guest internet access to the known portal check URLs, and your website, but block everything else. Captive portal becomes a click through. The real cookies and user customization are set once the device is back online in the full browser on your site.