Chemical compounds responsible for the colors in flowers?
are there other classes of compounds responsible for the red and yellow colors found in flowers?


Interest in colors, specifically dyes, was a real motivator for serious chemical work. Some of the early efforts were aiming to mimic Tyrian purple, also known as Royal Purple, because in antiquity it was worth its weight in gold.

Two classes of molecules come to mind other than anthocyanins in phytochemistry, such as the closely related flavones (its root means yellow) and the distinct carotenes (its root means carrot, but also responsible for flamingo color). 


  Can the red colors that give a "normal" anthocyanin pH response arise from pigments held in an acidic environment in the plant?


A real sharp organic chemist by the name of Richard Willstatter proposed this  in the early 1900s. He was working on determining the structure of the pigment responsible for the blue color in cornflower. He extracted the same substance coming from a rose and proposed that all flower colors were due to a different pH in the sap. As your experiment clearly points out, however, alkaline conditions are typically required for the blue anion. A Japanese group argued that alkaline conditions in the sap were unlikely and that instead these different colors can be explained by the formation of metal-organic complexes.

It wasn't until 2005 that a definitive crystal structure was determined from the cornflower pigment called protocyanin. It turns out that the blue color comes from a supermolecule containing one $\ce{Fe^{3+}}$, one $\ce{Mg^{2+}}$, two $\ce{Ca^{2+}}$, six anthocyanin and six flavone molecules packaged together in a complex structure. This color, as I vaguely recall, remains blue from pH 7 until pH 1! This agreed with some earlier evidence which suggested a complex species by the temperature dependence of the pigment.

These are not easy studies to conduct and I'm not familiar with how in-depth red colors have been studied, but it is certainly possible a complex species is actually how the red pigments form in vivo. Keeping in mind that plant vacuoles have a pH on the order of 5, we'll generally notice a loss in red above pH 3 in solution for a pure anthrocyanin in solution as hydration of the cation occurs. Stability of the color, and thus cation, obviously must be obtained either via copigmentation or with metals in a plant.