My guess is that if those who make these decisions thought it warranted four tracking it would have been done already. I was born and bred in Welwyn, and recall the subject being raised ever since I was a kid back in the late 60's. Back then the north bound divergence into a down and up slow occurred shortly after the viaduct at Robbery Bottom lane, but was then remodeled as part of the HST / Electrification programs, with the points being relayed after the Heath Road bridge, probably as the track is straighter ?
If you look at the land around the line between Woolmer green and WGC, it might be possible to change the path of the existing track so that two new tracks were laid to the east of the lines rather than run new down slow and up slow as there would be less need to purchase houses in Broom Hill /Woodland way area as there is just farmland to the east of the lines. However the big issue is Welwyn North Station, a grade II listed building... You might get permission to remove the existing platform on the down line and move it west to accommodate two new lines, but this would mean that the new tunnels would be to the west of the existing tunnels so the earlier idea of running the lines to the east of the existing lines wouldn't work, and compulsory purchase of homes in Broom hill would be needed.
I don't think it's the cost of building materials that's held up this idea, more the costs of changes to a grade II listed building, purchasing the houses back and given the area that is affected the complaints likely to come about on the environment. On a practical note, they could follow the Victorian example and use spoil from the tunnel to create the new embankments either side of the viaduct. The viaduct would also need to be built in the same style as the existing one and presumably side by side rather than widening the existing viaduct. One possibility would be to use the Hertford loop to divert trains and then widen the existing viaduct with a bus service between WGC, Welwyn North, Knebworth and Stevenage whilst this work is done.
Would be an interesting project to vlog