That's my point. Because he didn't ask for Picard directly, how would he know that Janeway would send him? For all he knew, she'd have sent any other ship. But as you said, he needed Picard. So I ask again, why didn't he just ask for him directly?
By asking, he would be revealing his weakness, and would have no future even if cured. All his plans about revenge would be ruined.
By setting things up so that Picard was the closest to the seldom-visited RNZ, he'd get his cure, he'd get it his way (Picard dies), and he wouldn't need to reveal his weakness to anybody (perhaps not even Picard).
Shinzon was dying. He wasn't interested in trying to impersonate Picard. He was trying to save his life in the most idiotic way possible.
Well, no. He was in no hurry in that respect: he spent what looked like at least a day just twiddling his thumbs and doing all sorts of utterly unrelated things, such as toying with Mrs Troi, intimidating his Romulan supporters, having tea and space crumpets with Picard, and hacking into Starfleet datanets. Plus he kept Picard waiting for
seventeen hours for unknown reasons!
Clearly, getting Picard's blood was pretty far down his list of priorities.
If you knew that you only had a few days to live, and you also knew that there was a person who's blood could definitely cure you, and that person was, say, the President of the United States, and say, that through some quirk of fate you looked exactly like Mr. President, and furthermore, that you had some object that the President wanted but which you could also potentially use to infiltrate the White House with, what would you do? Would you try to kidnap and kill the President by stealing his blood, then impersonate him and take over the White House?
If it so obviously was my lifelong ambition to either run the United States or then bring about its doom, sure I would...
Incidentally, it's a bit doubtful that Shinzon actually had only a few days to live when he launched his rebellion. Sure, the slowly approaching premature death would motivate him to act, but if the timing was of his choosing, he would have acted sooner. If the timing was not his choosing, then it would be too much of a coincidence that he would only have a few days to live.
Rather, it would seem that his bouts of anger hastened his demise (see all those vein-popping scenes!). Hence, a plan launched at an arbitrary moment would
result in him approaching death at an accelerating pace.
(Personally, I think that the moment for the Spartacus rebellion was dictated by orbital mechanics: Remus needed to be next to Romulus, which might only happen once per a few decades if the two worlds indeed orbit the star at very close yet independent orbits and Romulus has a slightly faster angular speed... The moment of proximity would be psychologically important if not logistically crucial for a slave rebellion intended to topple the Romulan government.)
Timo Saloniemi