Laundry room utility sink plumbing diagram questions!

[nholt]

Here is some background: I'm the Houston Texas area and we added a laundry room to the back of the house. It has a separate drain that connects to the sewer line in the yard and therefore it doesn't connect to the main drain/waste/vent stack in the house. I have a front loading washing machine then next to it is going to be a utility sink. Above the utility sink is a window. I am "furring out" this section of the wall under the countertop so I don't have to drill holes through all those 2x4s and possible violate a building code. Right below the countertop I was planning to curve the vent into the wall and up inside the wall just like the pex pipe is. Here is my questions: My original plan was to run the sink vent under the window under the countertop then connect to vent that will go up through the roof. However I was reading how the sink vent has to be a minimum of 6 inches above the sink rim before it connects to the main vent. The sink rim is just a few inches below the window. The green represents the sink in the photos. So I came up with a plan B which is to route the vent around the window but don't connect to the main vent until it is way above the sink rim. See my third picture. The red represents the window. But then how do I conceal that section without furring out the wall above the countertop? I need help! lol Also can I use "sanitary tees" on everything in the photos?