Montana's are one of the easier ones to propagate from cuttings. Here's a link that may help: Clematis from cuttings.

I used Clonex rooting compound, which, according to them, ....has a full spectrum of mineral nutrients and trace elements to nourish the young roots during their important formative stage.... " And from use with other plants, there's enough nutrients present that they'll grow noticeably in a sterile medium - in fact thats a sign that they've well rooted. I did try some miracle grow on a few to see if that would help. Didn't spray the foliage, just watered the vines with the proper dilution, but they just rotted within a few days. I received some very helpful correspondence from a Gardenweb member/reader (who I assume wishes to remain anonymous) who pointed out that cuttings from clematis taken at flowering nodes will root but won't shoot new growth, while cuttings with nodes further down vine that won't flower will be successful. I think that may be the issue.

carefully remove several of the lower "leaves" allow to air dry then apply 0.1% IBA (Rooting hormone)to "stem" stick in well drained soil & keep soil damp not wet..... the Leaves should be air dried & IF have a small cut area then also apply the same rooting hormone & stick in the soil There is a good chance it will also root. but both will be slow to root

Yes you can. I did this as well and it looked fantastic. Unfortunately, my armandii was in a pot, a half wind barrel, and after 5 years it outgrew the barrel and I had to get rid of it since I did not have a place to plant in the ground.. You have probably already noticed the shoots break fairly easily but this clematis is such a vigorous grower it doesn't seem to be much of a problem. I did not prune mine I just let it go... the deer did some pruning for me. Wonderful vine... I miss it.