My investigation on the matter
Ref #1
Staining known Gram-positive and Gram-negative organisms on either side of your unknown organism act as positive controls for your technique.
(Microbiology Laboratory Theory and Application (Michael J. Leboffe, Burton E. Pierce)
Ref #2
Similarly, cultures should undergo evaluation while they are still fresh. Old cultures tend to lose the peptidoglycan cell walls, which predisposes gram-positive cells to be gram-negative or gram variable.
(Tripathi N, Sapra A. Gram Staining. 2023 Aug 14. In: StatPearls [Internet]. Treasure Island (FL): StatPearls Publishing; 2023 Jan–. PMID: 32965827.)
Ref #3
Refrigeration impedes further growth of the bacteria, so you will have "fresh" cultures to work with during the next laboratory session.
(Laboratory Exercises in Microbiology By Robert A. Pollack, Lorraine Findlay, Walter Mondschein, R. Ronald Modesto)
Ref #4
Remember the following points concerning your [refrigerated or frozen] slant or agar stab stock cultures: -Do not use stored stock culture for making slides or routine inoculations.
(Laboratory Practices in Microbiology By Osman Erkmen)
Question
How do I create a sustainable readily available pair of stock cultures to act as Gram stain controls (as Ref #1), in the least time-consuming and tedious way?
From Ref #2 and #3, I can prepare two slant cultures, one is of a Gram-positive bacteria and the other is of a Gram-negative bacteria, then store them in the refrigerator or freezer. Then I can retrieve them daily and use them. After that, they are returned to storage.
However, Ref #4 argues against using refrigerated/frozen cultures for making slides.