Check out these guys in the Archdiocese of Chicago:

https://en.wikipedia.org/wiki/Canons_Regular_of_Saint_John_Cantius

I wouldn't say that they are "dedicated strictly to church music," but they are a very musical, traditional order with a number of professionally trained musicians among their professed members.

There are a few orders that come to mind:

1. The Dominicans of the St. Joseph Province (based out of D.C.) have quite a fine musical thing going on now — see here — as well as a serious vocations boom. I love the Dominicans!

2. The Fraternités Monastiques de Jérusalem à Montréal. The Fraternités is a remarkable order of men and women whose motto is, "In the heart of the city, in the heart of the church." They have been given numerous prominent churches throughout Europe, including in Paris (Saint Gervais), Mont St. Michel, Rome (San Sebastiano), Cologne (Groß Sankt Martin), Florence, Strasbourg, and elsewhere. They also have a church in North America — Blessed Sacrament in Montreal (Saint-Sacrement).

Their charism is beautifully sung liturgy, and having spent a few days in retreat with them in Montreal a decade ago, I can attest that it is overwhelming what 15-20 monks and sisters, facing the altar and praying together in song, can achieve — both aesthetically and spiritually.

While they have a couple visiting Americans and other English-speakers in residence in Montreal, the principal language there is French, and all the liturgies are sung in French. So if you're not a native French-speaker, this may not be the community for you. (I was visiting with a small English-speaking group from NYC.)

There's been some talk about getting them into the U.S., and much of their music — almost exclusively composed by André Gouzes, O.P. — has been translated into English. However, they're not here yet...

3. There's also the Community of Jesus, an ecumenical monastic community which runs a church in Cape Cod. The renowned ensemble Gloria Dei Cantores is drawn from members of the community, and has recorded over 50 CD's of sacred music, including ten discs of Gregorian chant and a wide variety of music by everyone from Mozart to Howells, Palestrina to Hovhaness, and nearly everyone in between. The choir does frequent tours through the U.S. and the world.

The Community of Jesus is not a Catholic religious order, but it is an organization with a very strong devotion to church music.

an ecumenical monastic community

How does this manifest itself?

In the Chicago area, the Benedictine Monastery of the Holy Cross is noted for its music practice.