For the sake of convenience I am answering this without any regard to your translation, or even no regard to the latter part of the sentence to begin with. So please have this in mind.
Having said that, let's concentrate on your posted question "X社の各部門を通じ", first.
Only then I feel like this is deceptively simple. Here's my answer.
** Through each related division of Company X**

Now second part:
ご関係の深いX社の各事業所ならびに（株）XCommunicationsにお配りしております。

This shows the direction of セールスプロモーションガイド. Obviously Company X has many sales or operation outfits in various locations (各事業所) which may be affected by the guidebook. It also has "XCommunications" as you explained.
The guidebook is distributed to all of the above through related division to them. So the distribution source is not one, but plural (divisions). I suspect the guidebook is not one single type, but with variation according to the above mentioned job duties, but it is only a speculation in this limitted context.

HTH

The promotion material is being passed out to the other 事業所(jigyousho) through each division of X company.

The head office of X company has a good relationship with 事業所, which can be understood as local branches that are under X company, or offices that have some kind of a contract with X company.

Hope this helps.