Felt like sketching a four-way version of this intersection after reading the Norwood Street signalizing post. This version of the intersection makes the 7th Street and Bailey Avenue western segments one-way-only exits from the intersection for one block. Green arrows are entries to the intersection (four entries total), and red arrows are exits (six exits total):
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One-way exit traffic from the 7th Street and Bailey Avenue western segments could be re-integrated into two-way traffic after one block via small traffic circles shown in yellow. Finally, current Norwood Street signalization is shown with a yellow cross.
I think this version I've sketched has been discussed a bit upthread in 2019; still had fun drawing it.
As a point of practicality, where do the inbound W7th and Bailey traffic flows go? In the case of Bailey a left turn onto (not very busy) 6th Street leads to a right turn onto University. Not too bad really. But coming down W7th, one would have to turn right onto Barden, then execute a left onto Camp Bowie. This would be problematic and would likely necessitate a traffic light at Barden and Camp Bowie that would have to be synchronized somehow with the larger signal a block to the east.
My impractical, pro-pedestrian, anti-car answer would be: I don't care what happens to the inbound traffic on these two roads, at all. I think fixing this horrible six-way intersection is so important that side-effects from the fix don't matter. If the city implemented my four-way version of the intersection with no budget or plan for side-effects I'd cheer and clap. But, I know this answer is unpalatable to motorists so I'll try to do a bit better:
A practical solution for Bailey Avenue inbound traffic: As you point out, Bailey isn't very busy so side effects from its effective closure up at W 6th Street would be limited. However, even traffic diverting east onto 6th from Bailey intending to make a right to run south on University to the intersection could pile up around the post office in an ugly way. I think Bailey commuters would learn to route around this, though, by diverting east from Bailey sooner, such as on 5th, or Bristol, or (why not) even White Settlement. Importantly, I think the intersection of White Settlement and Bailey could be rebuilt to discourage the Bailey "shortcut" to the six-way intersection: currently it's kind of built for crazy high-speed right turns from White Settlement onto Bailey and I really don't know what traffic engineers were thinking when they designed this.
A practical solution for W 7th Street inbound traffic: As you say, this is harder. The city could rebuild Barden between W 7th and Camp Bowie and plan for left turns towards the intersection, but this sucks because it's just pushing the problem one block away and probably destroying some local parking in the process. Instead, W 7th eastbound commuters will just need to divert south to Camp Bowie earlier, at Van Cliburn or even Montgomery, and make their way up Camp Bowie toward the intersection from a distance. Accordingly, I think the W 7th eastbound commuters will thereby have the greatest change to their driving habits, but I think this is okay because it has the complementary benefit of making W 7th safer for pedestrians in general—this is a benefit in addition to the local improvements of making the four-way conversion. Bailey was already a low-traffic street, but W 7th will be converted to a low-traffic street by pushing commuter traffic to Camp Bowie (where it belongs). And low traffic is good for local business, sidewalk life, and all the other benefits of walkable urbanism.