I'm not sure if any of these are feed stores or if they are open but they sound like feed stores. These are going to be your best bet for organic fertilizers. Sander's & Danley Feed Storeâ€Ž
2521 N Florida Ave
Alamogordo, NM 88310-5411
(575) 437-3820Alamo Feed & Supplyâ€Ž
2201 Eudora St
Alamogordo, NM 88310-6127
(575) 437-8703Hughes Farm & Ranch Supplyâ€Ž
7683 Highway 54 70
Tularosa, NM 88352-9698
Don't ask for organic fertilizer. Ask for soy bean meal or alfalfa pellets (rabbit sized pellets). Apply either one of those at 10-20 pounds per 1,000 square feet.
If you have alkaline soil, then you should adjust your expectations for the success of acid loving plants. If you want to succeed in gardening, the first rule is to grow plants that are adapted to your soil and climate. In your case that might limit you to smoke bush and wiregrass.