I don't know if I have the knowledge of this completely yet Leah; but I think the Progressed planets would suggest only a subtle type of hint as to what you may personally have changed into over the years when it comes to the personal planets.
(Sun,Moon,Venus,Mercury, Mars) in particular. For instance, do you "feel" those progressions, or do you still resonate moreso with your own natal from the year you were born? In some ways we will never get over the natal chart, but in subtle ways, we should at least "feel" we've changed over the years to resemble a bit, the progressed planets too.
As for Solar Returns, I am doing a few over on Zodiac Chat, and watching & commenting on them, for my daughter Becky who has had many changes over the past year since I erected her 2007 July Solar Return, and now her upcoming 2008.
I think I'm learning to respect the Solar Returns moreso, as a harbinger of what is to come and be felt in more then subtle ways, (almost in absolutes), in some ways, so I feel they are more correct when used as indicators of the immediate future. That is why I thought Rebecca's Solar Return, and that of her husband's should show us some fairly accurate and even "uncanny" results, because their lives have changed drastically since Spring of 2007.,when they moved 3,000 miles away for a new career and essentially everything has changed for them.
(some good, some maybe not as expected for her).......

There is however a book which should be read here first, to understand the complexity a bit of erecting and charting after it's erected the Solar Returns, as they must be (again); compared, contrasted to the Natal to see the issues that will come up
As for strength of influence of transits, I think they can be felt quite strongly, even when we think we;ve overcome our natal charts.
We are still as Edgar Cayce suggests, part of this solar system and universe, hence, he would have said, "Our destiny is and must be within the confines and context of this Solar System"
Meaning, when we die, we will die with Saturn, Jupiter, NN & Chiron, all meaningful, or some indicators, just as we might expect to find in our charts .......if we could see them at that time.
We can't completely escape the confines of the solar system, although a perfect Soul like Jesus, certainly did and could have saved himself, had he chosen to , IMO.
But since he was mortal, he too, both the life and the death can be charted by "reflection" of the transits to the natal.
They are (the transits of the planets) afterall, just vibrations, just as we ourselves are.
I'll be watching to see if you get some responses here, it will be interesting to see how each feels about your question.
Meanwhile, do visit Zodiac, and check out the Solar returns there too.,for hints...They are under, " our Natals".,
and here again is the chapter in the book:
see - *post 2 - "Planetary Triggers" by C. Teal