You are starting with a blank with dark coloration, and attempting to use a finish mainly comprised of boiled linseed oil, that penetrates below the surface.
Wood bleaches, typically contain oxalic acid, and rinsing and drying will leave the pores more open and more receptive to finish penetrating deeply.
I can tell you from experience, that if you took samples of the exact same walnut, and applied a coat of ten different clear wood finishes, you will end up with ten different appearances when dry.
When I conducted an experiment some years back to determine which wood glue would give me the strongest and least visible glue joint, I sanded and applied many different clear, untinted finishes to my Black Walnut samples to see what effect that had on the final appearance of the sanded glue joints.
I recall that Watco Danish Oil gave me the darkest finish, and a clear polyurethane was the lightest. There was quite a range in coloration in between, and the finishes that penetrated deeper tended to end up darker, while a spar varnish and an oil modified urethane tended to be lighter.
You might consider applying a moderately thinned coat of polyurethane as a first coat to act as a sealer, and then lightly sand back to the surface, and follow up with something else. You are doing the right thing by experimenting before getting down to brass tacks.
I also highly recommend getting a copy of the book, "Understanding Wood Finishing" by Rob Flexner. Used copies can be found pretty cheap, and you won't find more practical information on wood and wood finishing in one source anywhere.
