The plan is to have a budget of at least 350 HBD per month for each server in each continent.

Have you looked at Hetzner and Oneprovider? I don't know what their colocation rates are , but if you are figuring at each hbd is around $1 USD, those three servers will not cost that much including hardware rental (and Hetzner's are all with an i7 processor!)

For Hetzner look under the auction area early and often. I managed to grab one for a little less than 32 euro a month and I love it!

I actually left Oneprovider after a few years due to a panel issue and an unstable connection on one of their French servers but in general they are good and also cheap. A friend used them for colocation in the French datacenter and was happy. But be aware: With Hetzner you get a true 1 gbps or whatever you buy, while on Oneprovider you have to share your line unless you pay extra.

What panel issue did I have? Let's just say don't reboot from the panel unless you have to! It wiped my server for the first and last time after I had been there for years.