The filler you are using , 1/16" is really too small for what you are doing. Not sure what's going on with 3/32 with giving you issues. For me 1/16 is consumed too rapidly especially for a lap joint like that. You have to work twice as hard to cover the same amount of ground. Use your torch manipulation to push the wire into place with the 3/32 and about 75-85 amps.
If you are having to constantly push wire in with the lay wire technique, then its not working for you. I'd go to the dabbing method. The laywire is something that Jody has popularized that doesn't work for everyone. I've done it, and can do it, but not something I prefer..
There are two ways to do things when tig welding.
Adding wire with the lay wire, and then you concentrate on torch manipulation back and forth up down.
The other is to add the metal when you see a need for it, and just keep the torch steady.
Both produce satisfactory welds, but the dabbing isn't any more work to me than the laywire...It's just a different way of doing it.