Hellojaybobryan:
This type of question in slightly different formats has been posed over the last few weeks. Answers have been provided in relation to earth pressures for the design of the new wall. Some preferred active earth presures while others preferred at rest earth pressures with recognition of hydrostatic pressure if this was a concern.
The question you posed is very interesting and one which I have given a lot of thought to as I often get involved with evaluating performance of aged wooden structures and how to react to slopes that may fail at some time. The answer to many of these questions lie on your appreciation of the site and understanding of the historic behaviour of the wall in this particular case.
We are often faced with problems that we have very little understanding of past performance. However,unless in the boonies someone has some information to provide in my experience. So the first thing to do is to solicit this information. this may tell you that the wall is x years old and it has been the same way forever, etc. But you may see differently and that is usual from an Engineer's perspective.
Let us move on to your question and see what we can come up with. If the new wall is not at the verge of collapse but out of shape and hence seems to be deflecting or old etc, I would see first if I can apply some tiebacks to the existing wall.
Screw anchors if conditions are suitable provides a suitable application. Following this then, if my concern is to have a new wall outside for whatever reason, I would look at the distance away from the existing wall. If the distance is less than required for the soil to mobilize active conditions via the traditional 45 + phi/2 angle and this rupture line cuts into my old wall then I would use a much smaller value of earth pressure. What value to use is debatable and not readily obtained from conventional textbooks. A parabolic distribution can be used. Refer to pressures on silos, shafts, crib walls etc.
The design of the outer sheetpile wall is seen in my opinion varying from a curtain wall which is tied to the screw anchors to ensure against deflections etc, to a wall that is called upon to resist active or lateral earth pressures. I would not use higher than lateral earth pressures in these situations. Once the gap is filled between the walls, movement is reduced and failure becomes less likely as resistance is provided by the outer wall.
By this approach you can design an economical new wall in my opinion. Very often the question posed by the layperson is why do you have to design an elaborate and expensive structure. Very often these types of questions allow us to dig deeper.
The above are my personal opinions and my approach in any event is to examine all possibilities and then apply judgement.
Good Luck