Although I suppose it is not typical plug welding protocol, I would machine the top of the vertical piece to have a number of protrusions perhaps an 1/8" tall and 1/4" long that would extend through holes in the horizontal piece with the welds being between these extensions and the cross piece. My goal is to minimize the weld pool size in the cross piece to minimize the amount of melted steel that, when contracting during cooling, would cause the cross piece to warp.
I am no welding engineer but have seen warping when doing welds like this, especially long continuous welds. I have been able to deal with the warping with the big hammer but that does not seem to be a good way when you are looking for a nice finish.
Maybe a trial piece is warranted.
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