I went to the store, laid out all the parts, see that I have to switch the order. In the second try the Wye + Eighth Bend that plumbs the WC (which is rear-discharge, so comes out of the plane of the picture) connects directly to drain; the Wye + Eighth Bend that plumbs the clothes washer connects to the left of the WC's. Can I count on the washer's vent to vent the WC? Something seems funny about having a vent behind the direction of flow. Picture at [ibb.co]

The toilet would be wet vented by the clothes washer drain and that is not allowed. Only bathroom fixtures can be a part of the wet vent system. The toilet would need a separate vent and that can run parallel with the vertical clothes washer vent and tie them together at least 6" above the flood level of the standpipe.

Thanks. I thought about it more after I asked, thought it was a bad idea to have a vent upstream of a trap.

After more thinking I think I need a double wye with a 2" side inlet, with eighth-bends on the wye arms. Charlotte makes one in 3", part # 611S. The 'octopus', the part I already have, [ibb.co] is this, with the bonus that the wyes are 2", what I want. (The Charlotte's are 3".) I have to rotate it 45° and move it away from the west wall at least 9". I do that with an eighth bend the other way attached to a 90° elbow.

What you wanted to do is perfectly legal, if instead of the laundry standpipe, you had a bathroom sink drain. The toilet can be wet vented with another bathroom fixture.