Yes, importing is available via the following options: from clipboard or from file, optionally in RAW.
Btw sorry, you asked before if tx export was possible, for some reason I missed that option before.
Ahh well then, that changes everything! This should (hopefully) be the easiest option going forward then. What I would do is the following:
Get a list of all the addresses which still have funds on them.
Create a new Electrum wallet, select "Import bitcoin addresses or private keys", and insert all your addresses
In that Electrum wallet, create a transaction sending all those coins to a regular address you control
At the bottom left of the transaction window, select "Export" (you might have to select "Finalize" first), and export to clipboard
Import it from the clipboard in to mSIGMA and (hopefully!) sign it
Export it from mSIGMA, import it back in to Electrum, and broadcast it