Time to make plans and get the details for the antenna in mind.
I assume you are wanting to make a duplicate of the L4 with matching, right?
I noticed you have, what looks me like a coaxial choke at the driven element feed point area. I assume you are direct feeding at 3:00 or 9:00 o'clock using a small insulator out there at the end of the wires, and again, that looks to be feeding the conventional quad vertically, right? See page #9, of the old instructions from Signal Engineering.
The SE or LA's quads are voltage fed, and in that same position...the L4 would be feeding it for horizontal polarity.
Does that idea work?
If so, then work it as much as you can so you have plenty of experience using the antenna as a conventional Vertical quad.
I'm just guessing here.