Wet venting means you can run a shower or lav into a toilet vent on the same floor.
You can't run a toilet into a shower vent.
I would reconfigure and put in the vents. Frankly, you are talking about a few fittings, and then you know it will work.
I've seen plenty of homeowner and handymen jobs where they didn't understand the physics of it.
One grumpy homeowner was upset that everytime he drained the soaking tub, black gooey stuff filled his shower.
And when he dumped his kitchen sink on the other side of the house, the washer downstairs overflowed.
Handyman plumbing without the vents.
If you put your thumb on the top of the straw, it doesn't drain.
Plumbing is the same way. For every pipe going down, you need one going up.
For every trap, you need to vent it or it will siphon.
If you are letting water dump down a pipe without a way of air entering the pipe, you will be pushing a cushion of air downwards causing grief downstream.
A few fittings here would be really cheap insurance. And I think the layout in that tight of space is going to require more mind bending then usual.
Sometime that a 8,000 hour plumber can do in his sleep.