Okay, just firstly to clarify, its not that you "should" do another colourb4 a week later or even the same day, its just that you "can". You can actually do one after the other, up to 3 in a row, on the same day, if you like. But there is no harm waiting a week in between because you can assess the amount of reoxidisation you experience and if its not too bad, you can be pretty sure that you will get an even better result 2nd time round. Also, in a week the 8 wash can be washed out, so its a good time to do it again before putting another 8 wash in.
Right, OP, this is what I'd do if I were you, its not to say you will want to do it but this is what I personally would do seeing you have already coloured over.
I'd take a strand test of the darkest bit of your hair, somewhere underneath where you wont notice if you snip a strand off, secure it with a sticky label.
I would then buy some Jerome Russell "hair lightener" (i,e bleach) most chemists or tesco or whatever sell this even if its part of a highlighting pack. It must be 40 volume hydrogen peroxide and a sachet of bleach powder. Will link to that in a min.
High lift bleach
40 volume peroxide
Mix some product together in the correct ratio, paint it on your strand test generiously, wrap up in foil and put in a warm place for an hour.
Rinse it off, and see what colour it is. If you have managed to "lift" your hair to an orangey colour, it may well be similar to that of your roots, you are then in a position to dye all your hair one colour.
If that is the case I would apply newly mixed up bleach mixture to your ends, leave for an hour, rinse, and hello ginger, time to dye again.
You would then need to buy I reckon a dark ash blonde (you don't want to go too dark) - you can strand test that first on your old strand test as well - just to be sure - and you are sorted.
If you went to a hairdresser, this is probably what she would do - bleach your ends. Bleach isn't the end of the world, its fairly harsh and drying but one bleach won't hurt.
I personally think with black build ups and a 2 tone thing happening that you will get a better result in the long run if you just bleach out your ends.
What do you reckon? Is that all too scary?