It seems that you are some convinced, but someone in the organization is not empowering you to do it. As you can read from the other comments, you should do it.
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The most important factor is that your customers are forced to the last 'instable' branch and if your contracts with your customers makes you responsible for deploying instable versions, your company is losing money. You should really focus on release stability here. This is the main reason for source control, and as it seems your main failure. The others will not be improved that much by using source control as you already have alternative systems in place.