To be quite honest, it is very slow going with the 'mainstream' established dyslexia programmes. You could be talking 3 or 4 years! They do teach phonics, but they teach it very slowly and incorporate a great deal of unnecessary stuff, like putting out an alphabet arc at every session, chanting letter name, sound and clue word at every session, feeling wooden letters in a bag, learning word families & consonant blends, learning the 'rules of syllabification....
In the days when teaching reading was just about exclusively 'whole language'/'look and say, and phonics was a dirty word, the dyslexia programmes (which are all based on the work of Dr. Orton in the 1920s - so you'd have hoped that they'd moved on a bit from there...but, they haven't) were more successful than mainstream instruction; any phonics is better than no phonics. But modern Synthetic Phonics teaching is pacier and completely stripped of all the time wasting stuff which doesn't help children to learn to read. It is better than the 'dyslexia' programmes but the dyslexia people either assert that they are teaching synthetic phonics (which they are not) or ignore SP altogether.
If your daughter does have a memory problem then it will take a year, maybe two for her to become really secure with the phonics. It really depends on how much she already knows, how much she practices and how keen she is to learn.
The 'readable mess' is a complete red herring. For a start, it is an internet meme and has no sound scientific basis. Secondly, the only reason you can read it, as someone else has pointed out, is because you are a skilled reader and can do anagrams. If you believe that it is only the first and last letter of a word that counts then you are flying in the face of every piece of eye movement research which shows that skilled readers process all the letters in a word, sequentially, from L to R.
And you can't do anagrams until you are skilled at reading...
You say: "
There may or may not be other ways of learning to read - but there are definitely other ways of teaching to read."
I would agree only in so far as there are different techniques which children can use to learn how to sound out and blend words, and maybe for intesive learning of letter/sound correspondences, but the whole concept of SP is simple and it is its simplicity which makes it very powerful and effective.
BTW. I work with secondary age 'struggling readers'; in a school, so I see lots of them (between 20 - 40 in every new Y7 intake). Synthetic phonics has not failed me yet.