Angus:
I travel through Russia several times a year (delivering aircraft, my day job), and I can tell you that it is a MASSIVE pain in the arse to obtain Russian visas. Heck, I can get a visa for North Korea easier than I can get a visa for Russia.
Pretty much everything that the lady told you is true, except that the waiting period of 2 weeks seems a bit short (a bit optimistic) to me. I have my office obtain my Russian visas, and it takes about 8 weeks from start to finish of the process every year. Don't be surprised if they tell you that you have to get a HIV test as well, and submit the results with the visa application.
I cannot comment on your plan to try and get a visa in Astana, I have always applied for my visas in Canada (where I live, and my country of citizenship). But, honestly, I think you are screwed - I have never heard of anyone being able to short-cut the Russian visa process, no matter how much money they are willing to throw into the process.
Note also that to the best of my knowledge, a Russian transit visa is only valid for 96 hours (Edward Snowden excepted).
Michael
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