Plumbing for kitchen sink vent/drain

Please picture a L shaped kitchen when an existing sink on the interior wall.

I am now moving the sink to the exterior wall under a window.

1.
My plan is to drill the wall studs (doubled up) for the 1 1/4 sink vent, but I must somehow get over to the original wall to the existing vent line.
I was considering using 2 45' elbows just before the 90 degree angle and come out of the wall and back into the vented wall somewhere in the back corner of the lazy susan.
Does this sound like my best option?
I considered going up into the attic, but I don't think I have much work room between where the wall ends and the slope of the roof begins.

2.
I am pitching the drain pipe under the floor 7 feet along the joist then a 90' long elbow towards the existing drain another 4 feet (a total drop of about 2 3/4 inches).
Connecting the 1 1/2 pvc to the 1 1/2 copper with a vinyl coupling. Is there anything I should be aware of here. I have the coupling and it fits the PVC nicely, but the copper is much smaller in diameter Would a 1 1/2 to 1 1/4 coupling fit better?

Also does anyone see other issues that I have overlooked here?

Thanks,
Craig

Anyone

Please let me know what you think on this...I will be starting this project soon.

drain

1. Only you can tell if that is the best way, because you are there and we are not. But in this area the vent would have to be 1 1/2", partly because of code and partly because you wouldn't be able to find any 1 1/4" pipe or fittings.

2. Again in this area the drain would have to be 2" and you would need a plastic to copper transition coupling.

Just looking for 2nd opinions here, maybe more experienced views...
thanks for the comments.

Craig