Change reverb while keeping its parameters

Is there a way of changing reverb type (room, hall, cathedral..) while keeping its parameters unaltered?

The freezing tool works only if changing the piano preset, there I can keep the reverb parameters.

It doesn't work though if I stay in the same preset and only changed the reverb type, in this case the new selected reverb type will impose its parameters.

A workaround would be if it was possible to copy all reverb parameters (or some of them) and paste them onto the new reverb type, but I guess that's not implemented in this way.

Any ideas or suggestions?

Thanks,
David