We have 4 competing visual lines to contend with.
1. The house with a deck that extends out 10' (all straight)
2. A retaining wall that is concave.
3. A lakeshore that has a slight angle to the house
4. The East lot line is not parallel to the house.

We were out hours yesterday trying to find a happy medium using ropes. We haven't purchased the outdoor furniture yet, so we were having to wing it with what we had available. We're planning on purchasing.
1. 48" round table with 4 rocking/swivel chairs.
2. 2 rocking loveseats.
3. 4 zero gravity chairs

This is what we had for our old diagram which isn't drawn very well to the scale of the yard...it's maddening to try to get it right. We've adjusted it to include another 4' wide on either side of the patio. The front stone wall is drawn at a straight angle but IRL it's more concave especially on the right side.

Our last rope plan was to keep the depth the same but have the right side 1' less on the right side where the yard narrows.

On the left side where the end of the house is about 11' away from the lot line, at the end of the patio it would be about 14'. We thought we would angle the side closer to the lot line and make it about 12' on the patio end. This would leave put out patio into a slight trapezoid.

We're thinking this may be the best alternative but we'd like to know if there are any other alternatives we haven't already exhausted.

I wish I had caught this earlier (none of the designers did either) but at least the patio was hasn't been laid.

It's difficult to home in on the question with the excess of details. They are clutter and camouflage. Unfortunately, your sketch doesn't help because it's also cluttered with camouflage. While it may be fine for your own thinking process, it's not very useful for communicating information to other people. It's time to draw a new plan that is accurate and clean. Show edges of major elements & lot lines. Don't show details (plant clouds, patio stones, etc.) Make the scale accurate.