Is it possible to squeeze the hereditarily Cantorian world "$\sf H_{Cant}$" of $\sf NFU$ to be the hereditarily strongly Cantorian world "$\sf H_{Cant^+}$", and at the same time itself the well founded world $\sf WF$ of $\sf NFU$. Moreover, can we have $\sf WF$ of $\sf NFU$ to satisfy all rules of $\sf ZFC$.

In symbols:

Is "$\sf NFU + (WF \models ZFC) + H_{Cant} = H_{Cant^+} = WF$" consistent?

Where a well founded set is a set belonging to the cumulative hierarchy of pure sets. Alternatively one can work in $\sf NFU^V$ where all Ur-elements are co-extensional with the universe $V$, and use the usual definition of well founded sets.

If this is consistent, then what would be the consistency strength of such extension of $\sf NFU$?

Is it possible to squeeze the hereditarily Cantorian world "$\sf H_{Cant}$" of $\sf NFU$ be the well founded world $\sf WF$ of $\sf NFU$. Moreover, can we have $\sf WF$ of $\sf NFU$ to satisfy all rules of $\sf ZFC$.

In symbols:

Is "$\sf NFU + (WF \models ZFC) + H_{Cant} = WF$" consistent?

Where a well founded set is a set belonging to the cumulative hierarchy of pure sets. Alternatively one can work in $\sf NFU^V$ where all Ur-elements are co-extensional with the universe $V$, and use the usual definition of well founded sets.

If this is consistent, then what would be the consistency strength of such extension of $\sf NFU$?

Is it possible to squeeze the hereditarily Cantorian world "$\sf H_{Cant}$" of $\sf NFU$ to be the hereditarily strongly Cantorian world "$\sf H_{Cant^+}$", and at the same time itself the well founded world $\sf WF$ of $\sf NFU$. Moreover, can we have $\sf WF$ of $\sf NFU$ to satisfy all rules of $\sf ZFC$.

In symbols:

Is "$\sf NFU + (WF \models ZFC) + H_{Cant} = H_{Cant^+} = WF$" consistent?

If this is consistent, then what would be the consistency strength of such extension of $\sf NFU$?

Is it possible to squeeze the hereditarily Cantorian world "$\sf H_{Cant}$" of $\sf NFU$ to be the hereditarily strongly Cantorian world "$\sf H_{Cant^+}$", and at the same time itself the well founded world $\sf WF$ of $\sf NFU$. Moreover, can we have $\sf WF$ of $\sf NFU$ to satisfy all rules of $\sf ZFC$.

In symbols:

Is "$\sf NFU + (WF \models ZFC) + H_{Cant} = H_{Cant^+} = WF$" consistent?

Where a well founded set is a set belonging to the cumulative hierarchy of pure sets. Alternatively one can work in $\sf NFU^V$ where all Ur-elements are co-extensional with the universe $V$, and use the usual definition of well founded sets.

If this is consistent, then what would be the consistency strength of such extension of $\sf NFU$?