I have heard a lot of people attempt the tone with a rat, and so far, I am not a believer that the two share any DNA. It might fool some live, but I have not heard it.
As for the russian muff, yes, just get one. Bass Big muff is no where near the tone. I would add the BSW, and an OC-2 to that line up as well. P+C for Uprising and Helsinki Jam, and maybe an FM4, though I have yet to find those tones anywhere...
The animato is just different enough, that it is the tone. The SB1 truly has no replacement if copping the tone was what you where going for. The Korg G5 is comparable, but the sounds will not be the same. It truly is "the pedal" to get.