Bath sink vent options

I am remodeling a 3/4 bath. This is on the 1st floor of a ranch house. I planned on keeping the same layout and keep the drain piping in place. The walls have been gutted.

The problem is that the old sink drained through the floor directly to a 3" sewer pipe below. I wanted to redirect the 1-1/2" pipe up through the wall (outside wall) and continue a vent up into the attic to connect with the existing 3" vent. However, due to the shallow roof angle, hvac vents, and wiring I cannot access this part of the attic to do the pipe routing.

Now I am concidering my options. This is the only place I can have the sink, so relocation is out. The nearest vent runs up behind the toliet 6-1/2' away on the opposite side of the room. The toilet drain (3") flows towards the wall with the sink where it connects with with the 3" drain leg serviceing this side of the house.

Can I run my vent up 42" above the floor, back under the floor and connect to the toilet drain with a wye connector near the vent? There would then be about 18" of shared wet horizontal venting. Or, do I need to connect to the drain as described above, then continue the vent with a tee to connect to the vertical vent 42" above the floor in the wall?

Thanks for your advice in advance. I this is unclear, I will describe further or try a drawing

Brian

Cannot go down once you are going up with a vent, that creates a trap in the piping. Just take the vent through the roof, increase to 3", 12" before you go through the roof.

vent

You have to differentiate between what is legal and what will work. It will work the way you describe it, but it would confuse most inspectors and they would reject it.