Range hood vent wall exit location and duct transition

I am planning a vent run for a basic metal range hood for a standard 30" electric range. For the wall exit, I bought a 3.25 x 10 wall vent hood. I plan to locate the exit hole near the vertical center of a 9" tall rim joist. Reaching this hole will be challenging b/c it is located over a 24" duct that runs under and across the joist bay in a soffit. There's also a 2" pipe running through the right side of the same joist bay that I'm putting the duct in.

Running everything would be much easier if I could find a 3.25 x10 to 7 boot transition in the following shape: with round end facing u and the 10" end away from u, I want the round section to start flush with the top 10" side and flush left with the 3.25" side instead of centered left to right on the 10" side as is normal.

If this is not available, what additional transitions should I use to bring the 7" round pipe section over to the left so that it is flush with the left side of the bay and how far from the left side of the joist bay should I start my 10" exit hole to make the round pipe land flushed left after the transitions?

Thank you in advance for your help.

 

You can't go round all the way? This is an option. If the run isn't too far, you could run 6" out the wall. You would use a 7" to 6" adapter at range hood.

 

I thought I had to use at least 7" pipe for the duct, and would run 7" all the way until I reached the transition to hood piece. I assumed hood should use 10 x 3.25 to exit through the 9" tall rim joist.

If I have a 6" exit isn't that the same as running 6" all the way including a 6" exit hood with a 6" round hole in the rim joist?