There is no such thing as visa transfer process. When you’re switching jobs on an H1B you follow the same process as if it were a new application, with the exception it can be done any time in the year and the visa cap doesn’t apply.
Also, because it is a new application, your old one does not expire, so you can always continue your current job till you sort things out. And you can always file a third application with a third employer if things don't work out with your RFE. Changing jobs isn't as crazy as people make it out to be, unless you really don't meet the minimum.
PS: Been doing it for more than a decade without any problems