Bathroom remodel DWV

I am in the middle of a bathroom remodel. At this point the final configuration will likely be determined by the drains and vents required for a free standing tub, toilet and sink. The existing constraints include log walls which cannot have any plumbing, a single internal wall which holds the vent stack that continues through the roof, maintaining entry and exit points for existing 3 inch line. I also plan to use the internal wall for the tub filler. All other plumbing will be in the existing crawl space which will require putting p traps for both the tub and the sink below the sub-floor (I know not allowed). The previous pedestal sink had the p trap below the sub-floor and we never had any problems. The entire crawl space is accessible. Please look at my design and provide any recommendations. The biggest challenge is venting each fixture. The tool I am using seems to think it is ok to run horizontal vents to the stack. I'm sure this is not optimal. Also the tool refuses to run a vent to the sink. Our kitchen sink has an Air Admittance Valve which works well so I guess we could do the same but would prefer vent to the stack if possible. We are on a very tight budget so we hope to DYI all of the remodel including the plumbing.