No offense, as I know little about your website, but you're one site out of thousands/tens of thousands on Cloudflare at this point. Your results without substantial research and supporting evidence of this being a trending problem with other sites is not enough to say (per your article) 'As I mentioned earlier, avoid Cloudflare at all costs'.
First, have you contacted Cloudflare support regarding your purported page slowdowns? If not, they are actually very good about both fixing things and getting back to you, even on the piss-ant level plans.
Second, what optimization features exactly do you have enabled? Do you set proper cache headers? Those are especially important to Cloudflare and without them being properly set (especially on JS and CSS objects) I imagine your page speeds will be pure crap.
That isn't to say that Cloudflare is without issue. We've had them, they exist. But if you're going to present an issue and blame it on the service, do your homework first and present full evidence, otherwise don't spread it as it's just an unproven lie.
Yes, I have contacted Coudflare about slowdown issues. I tried to use Cloudflare across a few sites with many weeks of testing. I agree that they are extremely helpful and responsive. One specific support ticket was about the time it took for ajax requests to complete. Cloudflare was adding up to one FULL second of latency. I also mentioned response times reported by GoogleBot. They had no real answers. Though they did acknowledge some Ajax slowdown that was supposedly fixed.
Some days are better than others, but overall Cloudflare did not speed anything up. Perhaps free users don't get as good of a performance boost?
I had similar features enabled with Cloudflare as I do with Google PageSpeed. The sentence right before the one you quoted says: "The response times to the far left are a result of Cloudflare’s Full Caching features with Rocket Loader enabled.".
Essentially that graph shows what happens when all of Cloudflare's "CDN + Full Optimizations" features are enabled compared to most of Google's PageSpeed Service. It's the closest comparison that I can make.
Hard for me to say what happens for 'free' accounts. We only use pro or higher (A good number higher than pro). I would say not counting the additional performance features you get at the pro level, if they're purposefully slowing things down for free accounts that would be pretty crummy.
That still doesn't answer what you're doing with your cache headers. I took a basic look at your fantasysp site and I wonder if there isn't some changes you could make on the cache-control settings. You seem to be setting no-cache quite a bit.
You may want to avoid setting Expires to greater than 1 year, RFC 2616 (HTTP), section 14.21:
"To mark a response as 'never expires,' an origin server sends an Expires date approximately one year from the time the response is sent. HTTP/1.1 servers SHOULD NOT send Expires dates more than one year in the future."
If an agent is precisely following the RFC, anything set to more than 1 year in the future is an invalid date and:
"HTTP/1.1 clients and caches MUST treat other invalid date formats, especially including the value '0', as in the past (i.e., 'already expired')."
I just realized actually one very likely reason you would see a significant increase like this. I imagine that the GoogleBot and Pagespeed servers are on the same network, or at least regionally close enough to make a big difference.
Cloudflare is not going to be on the same network as Google for any of their servers as they host their own gear around the world. If you want to see the real speed decrease from switching it should be a set of tests between Cloudflare and Pagespeed from outside both of their respective networks (and a couple locations if possible). That would give you closer to real numbers... or the google services are on totally different networks and what you saw was real-world, which I couldn't answer.
Cloudflare response times to the far left and PageSpeed response times to the far right. I'm not sure what else to say.