Your problem is likely running the single drive, and I'm honestly shocked that things work great with 600 people online. Truly shocked.

There are a battery of tests you can run (iowait, iotop, iostat, for example) to see if i/o is the culprit, but I would bet a ton of money that it is. You have plenty of RAM, a heck of a quick CPU, and a really slow (I'm assuming it's a 7200rpm drive, not an old 5400rpm) drive.
RAID anything is going to increase your performance (and I would never recommend running without RAID anyway, but you know that I'm sure), but yes, the SSD drive should be a massive increase in performance for your forum. I personally would stick with the dedicated server over the cloud, because the resources are all yours. No matter how you slice it, a cloud/VPS/whatever is still "shared hosting" in a sense. The cloud drive array is probably going to be faster as far as i/o is concerned (perhaps a lot) than your single SSD drive, but I would still stay on the dedicated box. Ultimately, if your forum builds more and gets really busy, if the SSD drive doesn't cut it any longer, then you put 4 in a RAID10 array and call it a day. Not a big deal.
And to answer your other question, yes. Even a cheap consumer-grade SSD is going to get you around 50,000 IOPS (random). 1800/4500 is nothing.
If you've been a good long-term client, you might ask for a discount on the drive too. $75 for 100GB drive is insanely expensive. I mean hell, you can buy a 160GB Intel enterprise drive for under $150 these days, even cheaper if you buy in bulk. A <2 mo. ROI on the drive is a tad bit ridiculous. Never hurts to ask.

If they see that you're interested in upgrading, it likely means you're happy, and plan on sticking around for a bit.