Is Geologic Mineral Trapping of Chlorine Plausible?
One of the problems of geological sequestration of chlorine is that most chloride minerals are very soluble.

The number of non-soluble (or very little) minerals is limited, but there are several options. The obvious ones are sodalite ($\ce{Na8(Al6Si6O24)Cl2}$) and chlorapatite ($\ce{Ca5(PO4)3Cl}$). There are other options though.

Webmineral lists a lot of chlorine-bearing minerals, and most of those are soluble. However, there could be several minerals with high percentages of chlorine that are insoluble enough under the conditions of your reservoir. But in general, your best bet are anhydrous silicates and phosphates, because those are the most likely to be stable over a long time.

That said, this stuff could be dumped in the ocean. The $\ce{HCl}$ could be neutralised with something like feldspars, turning it into clay and a solution of harmless sodium chloride.

Alternatively, you can oxidise the HCl and make chlorine gas, a useful product.