Are there any sulphides, sulphates, carbonates that cannot be dissolved by aqua regia?
This was also asked in Chemistry Stack Exchange, where it was noted that barium sulfate is insoluble in water and generally insoluble in acids.  A quick check reveals that indeed the otherm minerals can be dissolved in nitric acid and so should yield to aqua regia.  Thus barite is the troublemaker.
Barite can be dissolved in hot alkaline chelating solutions, as described here[1].  This, of course, is not compatible with the acidic solvent you intend to use to dissolve and measure the gold.  It is not clear from the reference whether a pretreatment with such a chelating agent to remove the barite before placing in aqua regia would work when the barite is intermixed with the alkali-insoluble sulfides listed in the question.
Reference
1.
Bader Salem Ba Geri, Mohamed A. Mahmoud, Reyad A. Shawabkeh,  Abdulazeez Abdulraheem, &quot;Evaluation of Barium Sulfate (Barite) Solubility Using Different Chelating Agents at a High Temperature&quot;, Journal of Petroleum Science and Technology 7(2017), 1, 42-56.