I think Missoula is definitely not covered under any conceivable AA mileage award, since the Horizon flights carry no AA flight numbers and MSO is not even listed on the AA or OW flight directories as a valid city.
I'm also not sure if you could include Seattle en route to your transpac gateway; the small print in the AAdvantage T&Cs says
Tickets issued as AAdvantage flight awards are not applicable for travel on American Airlines cooperative codeshare service with other carriers. In addition, selected flights designated as AAdvantage airline participant flights, but operated by another carrier, may not be valid for award travel.
(My emphasis.)
which raises in my mind not only your abillity to use AS operated flights, but also JL, since AA flies its own metal over there.
So bottom line I suspect you'll need to pay for any flights to/from MSO, and for that matter
possibly the SEA or BOI (for access to MSO) segments as well, if the added routing takes you above the segment limits on the award ticket,
Looks like this is a job for your friendly AAdvantage rep. Good luck.