Washer and Vent Question

I need assistance on how to correctly vent a washer machine. I currently have the walls exposed on a home that I am remodeling and want to get opinions on how to proceed. The washer is a Spacemaker (compact) that currently has a 1 1/2" standpipe going into a 1 1/2" drain which feeds into the main house 3" drain that is under the slab.

The first picture is a graphical depiction of what I currently have and the second picture is my attempt at correctly venting the washer. The washer is currently 111" away from the existing kitchen sink vent and I know I need a vent < 3' 6" from the weir of trap for the washer. The second picture is my attempt at correctly attaching a vent in this situation.

I know that I should have a 2" standpipe and 2" drain but I can not get to the connection where the 1 1/2" drain connects to the 3" main building drain. Should I replace the 1 1/2" with a 2" and then I would only have a small section of 1 1/2" pipe feeding the main drain (less then 8").

Any suggestions would be welcomed.

The washer and sink should look this but with a co fitting in there somewhere.
The cleanout fitting for this one is below the picture and floor.

Of course the washer should have a 2" waste line and a 1.5" vent.
I would consider getting into the 3" line and putting a 3x2 wye in.

Thanks!

Thanks Terry! I see from your picture I have the San-Tee where the two vents connected inverted. I fully understand what you are saying about the 2" pipe, but there is just no way of getting in there without pulling the bathroom tub out in the adjoining room. In all honesty what are the chances of the washer overflowing especially since it is a compact stackable? This is the way it was plumbed before I took posession - I do not know if the previous owners experienced overflow. Since I may remodel the bathroom at another time, would it make sense to run 2" and just keep that 8" of 1 1/2" for the time being?

Thanks again!