Can we just take a moment to consider how LONG it took Dear Jim to plan The Great Game?
Painting an oil painting takes time. Imitating a master -- in such a way to successfully complete a forged painting -- takes time too. A considerable amount. The little old man mentioned in the show had to adjust his style to properly imitate what he meant to paint. He'd make some sample paintings. It wouldn't be something that took a few days.
Doing a successful forgery is complicated. For the purposes of the show, they did some handwaving over how experts would be testing a painting, researching it, comparing it to past paintings, etc.
(Okay, let's be honest, they did a LOT of handwaves. Realistically any specialist would have looked at the artist, his life, and what he was reputed to paint, and they'd've known long before SH that it was a fake.)
Let alone the other things, like the bribes. Sure, Jim probably invested a lot of bribes. He couldn't bribe everyone. But he could bribe enough people for a short-term scam to work out. Sort of.
If you look on John's blog, which we pretend has continuity (even though ACD was awful at that) then you see that barely two months passed between Study in Pink and TGG. The odds of JM having got it all around in that time... mm. Improbable.
I bet that Jim had dreamed up this little plot a long time ago. Years ago.
Maybe it was aimed at Sherlock, maybe not -- it might just have been the museum's owner's "Dear Jim" criminality. Or maybe it was just Jim's good fortune that it dovetailed into SH's own problems with astronomy.
I wonder if sometime Sherlock thought about how long Jim must've been watching him, and got the chills. It's a chilling thought.