www programming

Into this raw example, the integration code on page-forum.php has been changed so to not push urls into the address bar and return the same result of the one based on base64.
It is still not perfect under some aspect, just partially re-coded, so i would like to wait on showing it until the complete final code will not be ready.
Reloading you'll return on same page.
https://www.axew3.com/w3p/board/

I though about: why not to have a button that say: reload the board? So when necessary an user will reload the iframe, AND NOT the parent WP page.
This is useful because, supposing while writing a post, if the parent WP page is reloaded, the content of the iframed phpBB will be lost, together with the related browser history, while reloading the iframe and NOT the WP parent, the result will be exactly like to be into a full phpBB page not iframed.

So all really will result effectively fully working. Professional i would say.

But the WP Page still reloads while login?

?? possible!
I did not tested too much the thing, but sorry how did you get, and exactly what?

Without reloading WordPress after logging in through phpBB, the WordPress site still thinks you are not logged in.

I already tested it here. In my case, Safari asked me if I wanted to stay on the page or leave the page (which means reloading WordPress) when I used the phpBB login.

I understand the idea behind it, but especially for users like me, where parts of the WordPress menu are only visible after reloading WordPress while using the phpBB login, this template isn't very useful.

When i try to login, it present the dialog, then if you choose to not leave the page, it is obvious that then the WP parent page will not reload, and the user will result logged into phpBB and apparently not in WP.
But it could be maybe fixed, so to avoid the confirmation popup when the login/out occur.
It is a good point that should be fixed if possible (or in effect it would be not so nice maybe).

P.s and in any case it will never substitute the actual and default base64, it will be just a possible another way not included, that can be added.
I am not also totally sure that it will decently work.

The possible feature that will be possible to be added, is the draggable Reload forum (iframe) button:
having it on WP parent or phpBB is very easy and require few lines of code.
But as said, and like before, it will not included by default.

The problem about the parent WP reload and popup confirmation that you rightly reported, when the login/out is done into the iframed phpBB, has been fixed:
https://www.axew3.com/w3p/board/
It just do not fire anymore when a login/out into the iframed phpBB occur.
Any other eventual event conflicting with the correct parent reload (which i cannot imagine at moment what other could be, but surely could exist someone else) can be fixed in the same experimented (and working) way.

Ps. why did you not changed, into your site, the custom fancy URL (pushed URLs into the address bar) to be something like
.../forum/?surfing=dmlld3RvcGljLnBocD9wPTY1NTYjcDY1NTY=
and you're using the default w3 ....forum/?w3=dmlld3RvcGljLnBocD9wPTY1NTYjcDY1NTY=
??