fauxplumber..Judging by your layout details I must assume that the local code in your jurisdiction is based upon the International Residential Code. Your use of proper terminology and layout details sounds like you have been studying up on the codes, thats great.
Your local hardware gave you a bum tip. An air admittance valve (studor vent) may not be installed inside the wall cavity for two reasons. 1. Once the wallboard is applied there would be no access to air and 2. Air Admittance valves MUST BE installed in a readily accessible place for inspection or service. (Some jurisdictions will permit the AAV inside the wall cavity if it is equiped with a louvered & hinged access cover to permit air infiltration and service access.)
Air Admittance valves may be installed in the near proximity of the fixture being served or in the attic space. (when installed in the attic space it must be 6" above the level of the insulation).
You are correct that the line must be protected by a sleeve when it passes through a masonary wall, however, it must also be 6" below the average frost depth.
You did not mention whether the structure is on a slab or has a crawlspace or basement. Hopefully you have access under the floor.
You would not be permitted to make the temporary drain connection through the lid of the septic tank. All waste entering a septic tank must enter through the main drain line and all waste lines are required to have a minimum of 12" burial (In areas subject to frost the line must be 6" below average frost depth.) Also, there may be no connections to the main sewer line downstream of the house main cleanout at the junction of the house drain and house sewer. Immediately inside the foundation wall when there is a crawlspace or basement or on slab 3ft ourside the structure foundation.
The trap should be 6" above the floor to permit putting a catch pan under it to open the trap for service.
If you have access under the floor the International Residential Code will permit the trap under the floor. (The Uniform Plumbing Code prohibits traps under the floor)
The easiest method for you to create the vent would be to install an air admittance valve at the washer standpipe.
If the trap is installed on the end of a horizontal pipe the riser for the vent MUST BE connected by means of a WYE & 1/8th bend or Combo...TEE prohibited.
See Attached drawing.