Sounds particularly odd to me. Surely a change in orbital periods would affect the system dynamics in some way, especially if the periods of the inner and outer planets change at different rates.
As long as the removed mass is stored at a suitably great distance (or just discarded onto an escape trajectory), they won't change at different rates.
Storing large amounts of hydrogen in the inner system is more easily said than done (especially since, up to this point, at least, you are merely suggesting storing it somehow). Changes in the inner system don't bode well for me; I live there. Perhaps I'm just biased.
Read what I said again. I'm not suggesting storing it in the inner system. I'm saying that *unless* you store it in the inner system, it won't cause problems. The removed material is most likely going to be coming off the sun going fast enough that it won't remain in the inner system unless you take action to slow it down.
If, for whatever reason, you *do* store it in the inner system, then you are indeed at risk of seriously upsetting the dynamics of the system.
Of course, there's also the issue of reducing luminosity of the central star. I suppose in certain scenarios this would helpfully offset the natural rise in luminosity due to stellar evolution, but in other scenarios things may be more problematic (if for example a greatly increased stellar lifespan is only possible by reducing the stellar luminosity by a considerable amount).
The Wikipedia article on starlifting gives an order-of-magnitude estimate based on the depth of the Sun's gravity well that using 10 percent of the Sun's output you could remove about 6*10^21 kg per year, which works out to an Earth mass per millennium, or three thousandths of the Sun's mass in a million years. For comparison, with that energy budget, you could put Earth on an escape trajectory in a year or deorbit it into the sun in two. You've got plenty of time to tweak orbits (at least, you do if you have the resources to divert enough of the Sun's energy to make a starlifting project worthwhile at all).
Furthermore, the best candidates for star lifting (best increase in lifespan for least time invested) are high-mass stars that won't have habitable planets at the beginning of the project anyways. You *can* starlift the sun, but as the numbers above demonstrate, you really have to be in it for the long haul.
I don't see how changing the fundamental dynamics of a system (i.e. reducing the mass of the central body) is all that different from changing the fundamental dynamics of a boat (i.e. by creating hole in it and allowing water to enter a space previously filled with air). You may understand what is going on, and be able to bail out enough water to keep the vessel afloat, but you would still be better off if there were no hole at all.
Well, first of all, as I've said, as long as the ejected material is removed to a far enough distance, the dynamics of the system really don't change much (distances get scaled up by a constant, and the same for orbital periods). Secondly, unlike punching a hole in the bottom of a boat, you can stop removing mass from the star at any time, and depending on whether you stored the removed mass 1000 AU out or sent it on an escape trajectory, you may even be able to put it back. The difference is a much greater degree of control. (Plus, the timescale is long enough that you can monitor how things are going easily. In the Sun's case, you'll be several million years down the road before the effects start becoming noticeable).
