That is actually not true. SOME H1B labor isn't mobile (mostly people outsourcing firms), but people on H1B change jobs whenever they like. At least that's the norm in tech industry.
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