Hello Dan. Interesting problem, huh? I provide multisite hosting and support, so let's debug this ;)
You said the issues started when you upgraded to 3.8, and that you are considering downgrading back to 2.7.1. Do you really jumped versions from 2.7.1 to 3.8? You, brave!
If you were using WP during AGES, without a problem, and that was WP 2.7.x, I see two or three or six possible sources of failure :)
Are you keeping your server system up to date? Please tell me what are you using:
- PHP version: you should be using PHP >= 5.2.x. Recommended: 5.4.x
- Apache version: you should be using Apache > 2.x. Recommended: 2.4.x
- Server OS? Windows or Linux? If Linux, CentOS > 5.1. And please, be on a 64 bits OS to get the most out the memory performance. If Windows, well it should be at least Win 2000 Server with WAMP. Nope, seriously, use Linux CentOS.
- Server memory? if you are receiving 90k visitors/day, it should be > 2GB
- PHP memory_limit: better if >80MB. Ideally, 128 MB.
In the other hand, if you come from WP 2.7.x, your plugins are probably old enough and are breaking havoc in site performance. Browse via FTP to your plugins folder and tell me the date of the oldest, YET ACTIVE, plugin.
And how many active plugins are there?
Have you been upgrading those plugins?
In the other hand, if you own the server, you can try this: create another account, or even a subdomain for your site. Make a subfolder in its public_html folder. Save this page as HTML (or whatever you want, but plain HTML, low JS, low fat :) ) from your browser. Upload it to the folder we created. Browse to it! Is it slow? Is it fast? Tell me what you find there.
Two plugins I can recommend to see what may be going on, assuming you can still install anything:
WP-Memory-Usage: will tell you, in the Dashboard and in your admin footers, how many PHP memory is using every page, and how much is allocated via PHP.ini. It's a good start to see if your WP install is overloaded or your PHP badly configured.
P3 Profiler: this one is a great plugin which will analyze and profile your public and admin pages and tell which plugin is taking so much to load. Even the theme could be the culprit if you kept the same that was in use with WP 2.7
Well, hope to read your findings soon.