yes I think a bow will settle in after 1000 shots or so,,and has not revealed its true self until then,, I agree,,
Dances with Squirrels , I will try to answer the questions I have experience with,,
Yes I have kept shooting the bow after it shifted and it depends on the bow, and most of all the length of the bow( some bows won't shoot if you put the bottom limb up, the string is on the wrong side)
from my experience ,, the way a longer bow shoots is not as sensitive to tiller shift,, the bottom limb can be weaker and with nocking the arrow in the right place or adjusting the hold on the bow,, it will shoot fine,, good arrow flight etc,,,not a problem,,
some bows may require a slight tiller adjustment to get the arrow to fly as smooth as you like,,( some shooters don't shoot well enough to tell when the tiller shifts or not,,they may just be starting or have a poor release etc and have never seen an arrow fly correctly)
for me,,the shorter the bow,, the more critical the positive tiller seems to effect the way the bow shoots,, probably string angle etc and some things I don't understand, but I can feel it in the way the bow shoots and arrow flys,,,, not as well as a short bow with positive tiller for the way I grip and shoot a bow,,
I don't think having a bow with positive tiller causes the bow to shift tiller,, I think the way we hold the bow and grip the string will put more pressure on the bottom limb,, and the bow has to be designed to handle that,, if that is longer or wider or shorter draw ,,,
if the bow is being shot in high moisture conditions or stored as Badger explained,,,that could effect a tiller change as well,,
as far as your bows go,, a self bow may not reflect a positive tiller at brace,, but at full draw the top limb is weaker or working more than the bottom limb, and so shoots as if it has a positive tiller,,even though the braced profile does not show it,,