new tub vent vent or needs venting, wet vent?

I'm having to redo a bath so my MIL can come to live with us. She's 84 and has limited mobility. We found a tub that suits our/her needs.
The previous tub was wet vented to to the waste stack below the toilet and vented through roof behind the toilet.
The new tub's drain is now on the other end and is 5' from waste and vent. The question I have is wet venting the tub sufficient or should I add a vent for the tub that ties into the existing one. If so, would a 1 1/2" vent work or do I need to go with a 2" vent running from tub to existing vent stack

Putting in a vent line behind the tub isn't really doable because of load bearing issues and future water lines for tub spout and hand held sprayer. The most logical place to run it is through the same stud bay as existing vent


here's a pic of the tub and my rough sketch

Thank you,
Brian

905.3 upc

the vent shall rise vertically to a point not less than
six (6) inches (152mm) above the flood-level rim of
the fixture served before offsetting horizontally, and
whenever two or more vent pipes converge, each
such vent pipe shall rise to a point at least six(6)
inches(152mm) in height above the flood-level rim
of the plumbing fixture, it serves before being
connected to any other vent.Vents less than six(6)
inches(152mm)above the flood-level rim the
fixture shall be installed with approved drainage
fittings, material, and grade to the drain.

Yeah, the tub's vent line is wonky. Yes, I can (just barely) squeeze a 1 1/2" vent up that wall. There is an exhaust vent in that joist bay and the vent stack is in the next bay(vent stack is actually behind toilet-easier to draw it that way).
The tub drain is exactly 5' from the waste line below the toilet and is lead/cast iron with a 1 1/2" outlet for the tub drain. Can I just run 1 1/2" from tub to waste? if so, is the vent line really needed(can't it be wet vented for anything under 5')
Changing the cast iron 1 1/2" sweep to 2" sweep means having to snap off everything above the floor of the crawlspace. It can be done but spinal injuries limit my movement
I appreciate your and everyone else's attention to these issues. My mother-in-law moves in 30 days+/-
-Brian

draw exactly the toilet and tub are plumbed

better yet, take a picture and post it