I did well as did many others with Adsense years ago but the profit from that dried up over the past decade. That said If by 800 users per day you mean actively posting that is a lot of traffic and it may not be a bad idea to test to the waters with Adsesne if you want to go the advertising route. You'd have to let it go for a few months before drawing any conclusion, I wouldn't get my hopes up. There is also the privacy issue and ad blockers cutting into revenue.
There is the Viglink extension that comes with phpBB but I have no personal experience with it. I would be quite interested in hearing results from anyone that has.
Whatever the case direct advertising is where it's at if you can pull it off. I directly sell ads as percentage of the available advertising space on annual basis. Renewal time is coming up and I have 5% left.
It's custom script because you need to track the impressions. One of the difficulties involved with this is tracking legitimate traffic, since I'm not basing it on clicks or total impressions it's non issue. Other benefits include avoiding the privacy issue, avoiding the security issue and adblockers will not block them.
As far as subscriptions they are a catch 22, you can't attract new members if the content is sitting behind a paywall. The approach one very old forum I belong too has taken is a subscription for one forum. Long term members and new users happy to get the information may subscribe.
“Results! Why, man, I have gotten a lot of results! I have found several thousand things that won’t work.”
Attributed - Thomas Edison