"what does the expert think?"
The expert thinks he would like to have a word or two with the incompetent jackleg that mangled your basement rough in.
Now that we know that you were left with two traps and no way to vent the group let's see if we can get you out of the mess you were left.
Your idea of platforming the shower and arming out to the trap is about the only way to make it work. However you will still have to vent the shower. This MUST be done after the trap not before it as you suggest. I can't see any way around this except to go under the pour and cut a vent in downstream of the trap. The lavatory could be armed out from the stack in a half wall and the trap under the floor could be capped and covered over.
BUT, if you''re going to have to take up the floor to vent the shower why not take up the area and redo it the right way. Give me some measures. Would you have enough room to place the lavatory and the shower on the same side instead of having the toilet in the middle?
I don't see any way to use your present setup without taking up the cement.
Had the plumber not put two traps under the floor we could have worked out a wet vent situation but that went down the crapper when he installed the second trap. Sorry I couldn't be more upbeat. Tom