If you feel that the reason as to why your JIRA system is running slow is due to certain hardware restrictions, then indeed, moving to a cloud hosting could be a viable choice for you, as all the processing is done on the host side.
Atlassian actually has a cloud hosting service called OnDemand, which you can check out here - Atlassian OnDemand. Check out the page, and if interested, I'm sure our OnDemand team would be more than glad to help you set up your instance :)
I think that the problem is not related to JIRA being on your file system (behind the firewall), as the performance of JIRA is heavily related to the resources allocated to JIRA, such as memory, CPU, etc..
Perhaps, you would want to check those resources, and make sure they are enough to run JIRA smoothly. Here are some information on JIRA requirements:
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