I'm not sure they will be easily recoverable... mSIGNA uses "MultiSig" P2SH addresses for everything... even single signature addresses (They're set up as 1of1 addresses)... this makes it quite difficult to export the keys
The issue with P2SH addresses, is that you generally can't just "import a key" into another wallet and spend coins... you need to know what the original script was.
with the xpriv, there is a chance you could just recreate the private/public keys... and use something like coinb.in to create redeem scripts and craft manual transactions and sign them to be able to spend the coins... but unfortunately, I don't know what the BIP32 derivation path is for mSIGNA... I can't find any record of it being mentioned anywhere... and I've been looking through
the mSIGNA github without success... I'm not terribly familiar with C++ so some of the code doesn't make a lot of sense to me
At this point, your best bet is to try and get mSIGNA talking to your Bitcoin Core node so you can just send the coins out of the wallet. The fact that you sent coins before it was synced up shouldn't make any difference. mSIGNA should still be able to find them.
In the bottom right corner of the mSIGNA window, do you see something like "483594/483594" with a Green Tick icon?
If not, then it would seem that mSIGNA is not talking to your Bitcoin Node properly...
Also, if you manage to get in touch with mSIGNA support, maybe you can ask them what the BIP32 Derivation Path is