Opened the wall -drain pretty close to where I want the toilet-can I install a wall mount toilet here ?

[Mini Me]

Here are the dimensions measured after I opened the wall.

here is a previous thread that adds some context

For installing a new floating toilet is it easier to work from below when dealing with the old drain

Consider you have the layout in the first picture and consider that I want to replace the upstairs toilet with a floating one. For that to happen the plumber will have to do something with the drain for the old toilet and then cut the main stack (the blueish big vertical pipe) and connect the...

terrylove.com

Before opening the wall I made my peace with the idea that I will be installing a normal toilet because:
-I thought the wall is built with 2x4 studs (but no, it is built with 2x5")
-I thought that in order to reach the main stack (drain) I would need to go through a stud with would have been difficult with a carrier installed there and a 2x4" carrier

I am now seeing that:
-the wall is made using 2x5"s
-the drain is next to the toilet (as you can see it is a 3" offset)
I would prefer not to move the toilet to align it with the drain, if that is an option
Question marks:
-is it possible to connect the toilet with a T like fitting to still use the existing vent (that goes to the roof)
-is it acceptable to create adequate framing there to support the carrier (thinking about cutting the second from right to left stud and rebuild a frame there. Like so

-What do you guys use to transition from the toilet (ABS or PVC?) to the copper of the drain ?
-since I would have to probably relocate that horizontal dry vent for the sink and reconnect it to the main drain/dry vent I am thinking going ABS from the toilet T up to above the point where I would relocate the horizontal vent and then transition back to 3" copper using one of these flex couplings

I guess the biggest question mark is that T that connencts the toilet to the cupper drain (downward) and upward to more ABS pipe)
Update: here is a zoom in into what is behind the carrier

 

[Mini Me]

If I do not want to move the toilet sit to align with the drain I will have to use a 2x6 carrier (which allows the carrier elbow to protrude and pivot in the vertical plan at the back of the carrier. As per the below diagram for the 2x6 carrier the biggest quote front to back is 4 3/4" which will protrude in a wall that is built with 2x5 studs (5" is 4 5/8" as far as I can measure) Way too many complications to go for this. As the manual says the coupling of the carrier to the drain is also problematic to glue and I have only 3" to rotate that toward the stack which will need a Y there so way too little space for that