I drew a game in a similar way recently.

 Yep. I call it "loco rook", but it's basically the same thing. Also, just note that it's Re6+, because it the board were flipped black wouldn't be in stalemate, and a loco rook wouldn't work.

 So you know, that isn't actually drawn. I'll admit I just kind of assumed you were right at first, but after 3. ...Rh5+ 4. Kf4 Rf5+ 5.Ke4, there are no more checks with the rook that don't allow one of the white queens to move away fromt he stalemating position to capture the rook. You shouldn't have gotten a draw, heh.

4.Kg4 instead of 4.Kf4 works better because any check with the R loses? 

If 4...Rh4+ then 5.Qfxh4 wins. 

If 4...Rg5+ 5.Qhxg5+ wins (5...Kh7 6.Qg7#).

If 4..Rxh6 then 5.Qxh6 wins.

And any other moves allow 5.Qg7#.

 Heh, look at that. You're correct.