community of dyers

As long as you are measuring by weight, not by volume, and using identical dyes, the two companies' dyes will be the identical strength, as long as they are reasonably fresh (preferably less than one year) and have never been stored in a hot place, which would make them go bad quickly. (Also, dye strength will be reduced by how long it's been since you dissolved it in water.)

Look at my chart of Which Procion MX colors are pure, and which mixtures?. Jacquard's Procion MX type dyes are listed in a column under their parent company's name, Rupert, Gibbon, & Spider. You can see which dyes are the same. Any dye colors that are not on that page are proprietary mixtures, different for every company.

Two of the dyes you list are not equivalent. ProChem's mixing red is red MX-5B, which is not carmine red. Carmine red is a proprietary mixture made only by Jacquard. Jacquard uses the name magenta for red MX-5B. Most of your dyes are equivalent as you list them, though.

The dyes that are on the chart as being the same are the same strength, by weight. All Procion MX dyes are standardized by weight, not by volume. The dyes in one jar may be weaker or stronger from another jar, if you only measure them by volume, because different dye lots may be diluted to standard strength with different powders. The diluant Tamol is "fluffier" than the diluant sodium sulfate. Also, different lots of dye before dilution may be stronger or weaker, and thus need varying amounts of diluant to be added. This is true not only for dyes from different sources, but for different dyelots from the same supplier. The dye you buy one month may be weaker or stronger per teaspoon than the same dye you bought from the same source in another month, but they will both be the same strength per gram. You'll need to buy a scale to weigh your dyes, if you want consistency between different dyelots.

ProChem says to use roughly 5 tsp (or exactly 13 gm) of dye powder for a five-pound washing machine load to produce a pale color; roughly 5 Tbl (38 gm) of dye powder for a five-pound washing machine load to produce a medium color; roughly 10 Tbl (or exactly 75 gm) of dye powder for a five-pound washing machine load to produce a dark color; and roughly 20 Tbl (or exactly 150 gm) of dye powder for a five-pound washing machine load to produce black. Use one pound of salt per pound of fabric for light colors, or two pounds of salt per pound of fabric for dark colors. (See Immersion Dyeing in the Home Washing Machine using PRO MX Reactive Dyes.) This is for a top-loading washing machine. Your washing machine load size of 8 gallons is unusually small. Is it a top-loader?

-Paula