ZAB Controller reported a spill-out of a drone which was an airborne conflict with a commercial aircraft; and also reported about the complexities of the airspace.

Narrative

Weather exploded east of ELP; traffic quickly began to overwhelm the controller on Sector X who was working Aircraft X. Frequency congestion was a nightmare; the gigantic sector; the multiple transmitter sites; the planes all calling to deviate; and the bottleneck around ELP; Mexico; White Sands Missile Range (WSMR). The Controller was extremely busy; I was listening to him go down the tubes. I started out on the D-side on Sector Y and we were quickly in the same boat as the Controller on Sector X. Sector X Controller realized too late that Aircraft X was deviating north towards [Restricted Area] R-XXXX which was active FL300 and below. After taking the hand off; I realized the same thing; the Sector X Controller gave a hard vector south to a 190 heading and used the term immediately. I saw conflict alert go off with the Aircraft operating in R-XXXX; which we think was a military drone. The TCAS didn't go off on Aircraft X. The Pilot of Aircraft X checked on stating he turned south to miss a drone; not sure if that was an evasive maneuver or from the heading given from the Sector X Controller.We had to go into no notice holding as we got so busy; we couldn't insure separation of aircraft from each other or the White Sands Missile Range (WSMR). The weather quickly built and traffic quickly overwhelmed the SE specialty. Command Center / Traffic Management Unit (TMU) constantly neglect the complexity of us working traffic through this area. There is a lot of pressure for us to not hold; not lower the map numbers; not route planes north. I would recommend that we have a specific Pro-day for the SE and SW specialties to practice different routes and holding scenarios; and also have upper management encourage us to take this action sooner rather than waiting and trying just 'make it work' or 'just get through this shift'. There is a pernicious attitude that pervades both the SE; management; Traffic Management Unit and ZAB as a whole to never do this; that we change this culture.