Yeah, I'm having second thoughts about my third concern, the one regarding the money. It seems to me that a high noble might want to grease the wheels of the planetary government by making financial donations to people in key positions. He might also want to build up the Imperial brand by making various donations to both charity and public works. It sort of reminds me of the parable of the ten talents, which Richard mentioned earlier. If the higher-ups see the noble using his income to advance Imperial interest, he's more likely to retain his position or move-up when there's a vacancy in the hierarchy. Hence, all the high nobles would be incentivized to not squander their income, though, in practice, I could easily see the bribery and gifts going up the chain of command rather than down, so as to more directly ingratiate themselves with the people who ultimately determine their fate.
As for the 1% of GDP toward the Imperial military, this doesn't seem so awful given that there are thousands of worlds contributing. After all, the whole point of the Imperium is that individual worlds won't end up in an arms race with one another, freeing up GDP for stuff other than military spending.
Having said that, the idea of the commander of each regional fleet making 1% of 1% of GDP seems somewhat egregious. In a $100 trillion world, which we are fast approaching, he'd be making $10 billion per year just from a world like ours. The Constitution says this money is to be "retained by him in trust for payment of future pensions and benefits," but the question is who's pensions and benefits, given that he has thirty-three times that amount to spend on his own fleet. Is it his personal pension and benefits? Because if it is, then that's one hell of a golden parachute. But once again, if we assume that the higher-ups are watching what's going on down below and will remove him (perhaps with extreme prejudice) if he disburses money in a way that is contrary to expectations. then the whole thing can work, but like any system, it all depends on there being competent and moral people at the top of the food chain.
I guess there's pretty much no way around this requirement.