score:2
Even Rome2Rio suggests the only way is to fly to ANU (Antigua) and then you're needing to get from there to MNI.
That's an hour flying, which immediately pretty much rules out any other transport (obviously can't drive/train, so boat is the only other option and it's too far for a day trip).
Conclusion: you're going to either need to cough up for a charter flight, which won't be cheap, or fly via Antigua, staying overnight at least somewhere enroute or in Montserrat.