With dyeing, there is always a chance of an unpredictable outcome ;-) but I think it can be done. Monte Cristo is 100% cotton and there are chemical dyes that work in cold water, giving you an option to use a big container (garbage bin, or .....) which allows for the blanket to really move around in the water to get even colour spread. If you have a bit of Monte Cristo yarn left over, I would certainly dye a sample to see if you would get a good result before moving on to the blanket. Dyeing a fluffy yarn could be a different result and it would be useful to see how the Monte Cristo behaves in a dye bath! Let us know your results!

Maybe you can embellish instead? Like a fabric edge binding or stitch a design into the fabric?

In natural dyeing, they that advise yarn/fabric be scoured before mordant (if needed) and dyeing otherwise you get uneven results as well. Scouring can make the one blanket smaller?

Btw— make sure your embellishment is color fast or at least prewash or add a color catcher. I’m thinking of my “I should know better” quilting moments.