How thick will the concrete deck be below the 2" asphalt wearing surface?
Is this a bridge on private property?
Do you have a desired load rating?
Is your question about the beam size or the method of splicing the beams?
You can't drive a dump truck over corrugated metal deck without concrete fill.
I will check the beam size, but not the deck. I will comment qualitatively only on the beam splice. Is that reasonable?
Assuming your beams are W12x26 and each tire load is equally shared between two beams...
It almost works for strength, but deflection is about 1.5". That is too high.
The method of splicing you describe is reasonable, but the weld from the plate to the beam and the connection between the two end plates must be properly designed.
The metal deck diaphragm?
Those beams would be brace beams, not a diaphragm. They will not help with deflection.