Gordon syndrome: This condition, also known as pseudohypoaldosteronism type II, is characterized by hypertension, hyperkalemia, and low renin and aldosterone levels. The clinical presentation matches the scenario provided, making it the most likely diagnosis.

Liddle syndrome: Although Liddle syndrome typically presents with hypokalemia due to excessive sodium absorption, some variants might not fit the classic electrolyte imbalance profile. However, the presence of hyperkalemia in this case makes it less likely compared to Gordon syndrome.
Conn syndrome (Primary Aldosteronism): Typically presents with hypertension and hypokalemia due to high aldosterone levels, which contradicts the low aldosterone and hyperkalemia in this scenario. However, it's worth considering in the differential due to its impact on blood pressure control.

Renal Artery Stenosis: While not directly implied by the low renin and aldosterone levels, renal artery stenosis can cause difficult to control hypertension. The hyperkalemia could be secondary to renal impairment. Missing this diagnosis could lead to inadequate treatment and progression of renal disease.
Adrenal Insufficiency: Although less likely given the hypertension, certain forms of adrenal insufficiency can present with hyperkalemia. Missing this diagnosis could be critical due to the potential for life-threatening adrenal crisis.

Bartter syndrome: Typically presents with hypokalemia, alkalosis, and normal to low blood pressure, which does not match the scenario provided. It's a rare genetic disorder affecting the kidneys' ability to absorb potassium.
Other genetic disorders affecting renal electrolyte handling: There are several rare genetic conditions that could potentially lead to the combination of hypertension and hyperkalemia, often involving complex defects in renal ion transport mechanisms. These would be considered only after more common causes have been ruled out.