In short answer there are a couple of players in this market of Hybrid Clouds.
Providers that come to mind are Terremark, Rackspace, Logicworks and Amazon as you have mentioned. I know Softlayer does a lot of work on the development side I believe that is where they are at the strongest selling point.
If you have an RFP available after shopping around it may help in scaling out a solution and planning future growth. Check to see what each one has to offer, what differentiates them from one another, if its price, expertise, understanding of your needs as well as capability to deliver.
If compliance or any other regulations become necessary that would also be a deciding factor I would consider.
Of course all of these providers will want to win your business so it is most important to stress what you need for your operations to run such as you have mentioned 24x7 technical support.
Also to get more granular on a response I'd also recommend asking what tier is the support that they offer and if it is a help-desk level 1 engineer with escalation level 3 on a callback basis that may not be the proper solution.
I have heard about the floods in the datacenter and other similar disasters if this is a mission critical application as it sounds i'd also recommend working with one whom also offers not only the industry standard of a datacenter today but also a disaster recovery proposal for your needs with a failover process.
If you would more specifics or a recommendation shoot me an email or your phone number and I would be more than happy to speak with you.
Best of luck,