May I suggest that you create and sign the same transaction in MultiChain (using createrawtransaction and signrawtransaction passing in the private key), and see the difference between the two signatures?
The issue may well be related to "non-canonical DER signatures" which Bitcoin Core became stricter about a few years back (and this was inherited by MultiChain). Lots of explanations are available online, for example:
https://eklitzke.org/bitcoin-transaction-malleability