Your first issue is you have no equipment grounding conductor. There is no exceptions, if this is changed to a sub panel you will need to supply it with an equipment grounding conductor.
Another problem is if this was previously using 310.15(B)(7) for ampacity selection, it must still be supplying the entire dwelling load to still be able to use 310.15(B)(7). Now you could reduce the overcurrent protection on it if the load allows, but IMO the lack of an equipment grounding conductor kind of trumps this issue.
A couple other ways around this are to supply 240 volts to a transformer with 120/240 out - but you still need to bond the secondary to the grounding electrode at the service somehow, plus the transformer is likely to cost more than other options, or if there is no 240 volt loads and the 120 volt load is low enough - you could supply it with 120 volts only.