There are software products that can emulate a Metacode printer and tranform it so as to print on a more recent printer.
A quick search found these :
HostServe
RSA M.I.S. Print
XCHANGE printer emulation
There is also software to convert Metacode to, for example, PostScript :
Xerox Transformation - Convert DJDE, LCDS, Metacode.
It is highly unlikely that one may find a printer driver that produces a metacode file. Also, a 16-bit program from Windows 3.11 cannot run at all on 64-bit Windows.
To avoid these portability issues, the best solution might be to create a 16-bit virtual machine and on it install Windows 3.11 and the 16-bit metacode printer driver.
Almost all vitualization products allow the creattion of a virtual serial port on the guest that actually outputs to a file on the host.
This printer port, only usable inside the guest, may possibly be used to create the "Metacode printer" that you need. The generated metacode file on the host can then be sent on to be processed on the mainframe, as is actually your procedure.
If you still have the old Windows 3.11 computer, you could virtualize the physical computer to virtual (P2V), by virtualizing its hard disk and then attaching the virtual disk to a 16-bit virtual machine. This way the old Windows 3.11 setup will keep forever in its VM.
The Windows 3.11 VM doesn't need to connect to the network. The metacode file written to the virtual port is on the host, and it is the host that will connect to the network. The Windows 3.11 VM can be connected to the host-only virtual network adapter that is supplied by your virtualization product.