Thanks for all the ideas. I think between this thread, posing the same question on FB, some MgT books, and the trade tables on David Jaques-Watson's site, I think I have my answer. Since this is a T5 campaign, the MgT material will need some converting but, from what I've read so far, that looks to be trivial.
Some of you suggested I throw some spanners in the works. Here's what I'm doing:
The players are Traveller newbies and the game is set in the Regina subsector at the end of 1106. The asteroid is in the 871-438 system (Jewell subsector) and for 'reasons', they won't be able to act on this until early 1108 ... and they have no idea the 5FW is about to start. In other words, it's going to be behind enemy lines during a war. Currently, they have an unarmed detached duty Type-S (no mining equipment and a really small cargo hold) and none of the PCs have any experience mining. Plus, of course, they'll almost certainly be re-drafted once the war starts. Is that enough spanners?
Obviously, the logical solution would be to just sell the claim (and before the war starts) but that's not their plan right now. So I'm thinking of introducing them to a small mining outfit they could team up with. That should make them happy until the other shoe drops.