So the deposit for our Kili climb is paid! OK, we didn't actually have to wire money to Africa, rather it was going to Cyprus (but is that really any less shady!?). Our European trekkers (Ed and Imogen) assured me that people wire transfer money in Europe all the time (of course they were probably drunk at the time...) and this seems to be quite the reputable outfitter, so I'm sure all will be well, despite the initial trepidation.
After loads of researching different climb outfitters, we have selected Team Kilimanjaro as our trekking agency.