I am forgetting that mSIGMA has not been updated since 2017, and that Electrum exports transactions in PSBT format, which was only released in 2017 in BIP174. I wonder if this is the issue.

Why not try importing your addresses and creating the transaction using https://www.coinb.in/#newTransaction instead. This will export your transaction as plain hex, which is hopefully the format mSIGMA uses too, and then try importing that mSIGMA for signing?

If that fails, then I think the easiest thing is going to be to try to sync your mSIGMA wallet with NotATether's node as he kindly offered above.