The Midway is a bit rough, but usually the further one is from University/94, the better. I'd expect an altercation like this over on Dale and University. Still, all the traffic on Snelling can cause trouble. I avoid it. Unfortunately, there are very few good north/south routes in St. Paul's Midway to cross the interstate and railroad tracks.
First, let me say that I have not biked through over there. I cannot say 100% whether this would work, or how safe it would be. But I took a look at my bike map, as well as google earth and microsoft maps, and it looks like there might be a few alternatives.
I couldn't find anything west of Snelling for quite a ways. But Hamline Avenue is about 6 blocks east of Snelling. It appears to be a half-baked but perhaps usable bike route. It goes from north to south until it hits the north railroad tracks. It looks like perhaps people do a pickup-and-carry thing over the tracks to the parking lot on the other side -
http://maps.google.com/maps?f=q&sour...,157.22,,0,0.7
http://www.bing.com/maps/#JnE9LnN0K3...QuMTM3MTM4MzY2
http://www.bing.com/maps/?v=2&where1...20MN&encType=1
From there, you could take the streets a short ways to the bike/ped bridge over the south side of the tracks -
http://maps.google.com/maps?f=q&sour...,358.19,,0,7.1
http://www.bing.com/maps/?v=2&where1...20MN&encType=1
And continue on Hamline Ave going south over 94...though I admit, I don't know how busy it is.
And farther east Lexington has a dedicated bike path alongside it (even has a tunnel under the tracks) for the stretch that goes over the railroad tracks.
I dunno, just my thoughts - no totally ideal solution perhaps. :-(