Sorry for the delay, but we needed some time to clarify your question.
If you finally received the business invitation, I'd go with it, because it was still valid at the time of issue, and it doesn't really matter the father of your girlfriend has quit his job – seems like a more legit option to us.
The tourist voucher could also work, but I don't know which company you used and if it doesn't have a hotel included, this is a bit weird. The problem here though is that if you're getting a tourist invitation the purpose of your trip should also be "tourism", but you seem to be traveling for private reasons. Don't you want to ask your girlfriend to simply make a "private" invitation for you (it takes 1 month to process though, so it's just enough time) and have it mailed to you by courier, so you can apply for a private visa? In your case it would be the right option, I think.
If the time is a bit tight, you could simply get another tourist invitation, this time with a "homestay" listed as a place of stay. For instance you could request it through our partner company on http://waytorussia.net/Travel/VisaSupport.html
– ask them to put the right accommodation after you make the payment (you'll see their contact details on the payment page).
Hope it works out for you and let us know if you need more help!