Water seeps through basement floor at drain exit during heavy rain
1.  Some water might be tolerable in a minimally finished old basement.

In St Louis, a lot of houses would sometimes get some water in the basement.  Some of them a fair bit.  If this is going to destroy the berber rug in your man cave that is one thing.  If it is going to make a small puddle that is another.

If a little water entering the basement of your old house is not going to cause trouble, you could watch for it and mop it up.  You could seal the concrete floor of your basement.  You could set up a dehumidifier over a drain.

2.  You might be able to figure out why the water is coming in.

In the St Louis house there was part of the stone foundation fall that let a trickle of water thru.  I worked and worked on that wall.  It turned out that the reason it was letting water thru is that the gutter above was letting water fall down against the house, which then pooled against the house.  Fix the gutter, no more water thru the wall.  

When it is raining hard, go out and walk around (like the manly Midwestern homeowner you are) and see how the drainage is.  Is it pouring past a loose gutter?  Have misguided yard rehab efforts caused a change in drainage?  If you can see where water is getting up against the house, that might be where the water is tracking down, under, and then up thru the weak point by the pipe.  I actually figured out about the St Louis house gutter because of a spot by the house that was all sandy with no vegetation.  It had been scoured clean by the water coming past the gutter during hard rain.  I was suspicious and then confirmed it with a walk in the rain.  

I like the pipe photo and pipe stories, by the way.  Old houses are cool.