Awesome. Progress is always good. Problem solving isn't always fun.
Talk to your host again, ask them to peek at their server logs and investigate 404 errors on your domain. They will be able to tell you if the 404 was produced server-side if it's in their logs and why.
As for phpBB throwing Wordpress 404 page, I'm going to guess that maybe your file structure has Wordpress installed on a your main domain, and phpBB within or under that. As I said, it's an educated guess.. if phpBB is installed within your Wordpress file structure. For example, here is my file structure, with Wordpress on my main domain, phpBB installed within the file structure setup on a subdomain:
http://prntscr.com/j6xgot
There you see my /forums/ folder, that's my live phpBB sudomain, installed under my root, which is my Wordpress install. Near the bottom you see the /wp-content/ folder providing you the proof that this is exactly how I have mine. (However I never had this problem)
Now, I'm not saying change your file structure at all, as long as it's organized for you. But I'm saying, I think that's why it may be throwing the WP 404 on your forum.
Regardless, I'm willing to bet now with the new info you provided, it's because your being throttled, and that's why it's so random and can't be reproduced on demand.
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