One of the problems with using a standalone server with Biztalk360 is the unavailability of assemblies. When you load the business rules page in Biztalk360, you may find it inaccessible with various errors stating that various assemblies could not be found.
To solve this, grab all dll's for any custom BRE components you use in addition to all the dll's under C:\Program Files (x86)\Microsoft BizTalk ESB Toolkit 2.1\Bin from another system if you use the ESB toolkit. A simple way to gac these assemblies on a server which doesn't have access to Gacutil is to copy these dll's to C:\Windows\assembly. At this point the problem still persists and I've tried restarting the Biztalk360 service. In the end I couldn't figure out how to get Biztalk360 to access these dll's. Wait another 24 hours at which point Biztalk360 will have access to the dll's and will work correctly.