Okay, let's try and work this out. (Warning: this is very much a back-of-an-envelope calculation; corrections and comments appreciated.)
The plan, I believe, is for the 3tph that terminate at Longbridge to be extended to Bromsgrove. Judging by the current running times of 323s between Longbridge and Barnt Green, and by current running times of 170s booked to call at Barnt Green and Bromsgrove (namely
1V22 and
1M76), the journey from Longbridge to Bromsgrove should take about 9 minutes, with perhaps 11 minutes for the return working to account for climbing the Lickey.
Currently the Longbridge terminators arrive at xx13/33/53, and the Longbridge starters depart at xx22/42/02, with the units doing a shunt at Longbridge. That shunt won't be necessary at Bromsgrove. Even after allowing a few minutes to shoehorn it between the various XC paths, it looks the xx13 arrival at Longbridge could make it to Bromsgrove for about xx23, start back at xx31 and form what used to be the xx42 departure.
In other words, each Longbridge terminator effectively steps back by 20 minutes by going to Bromsgrove and back. By my reckoning that means you just need one extra unit. (I did check the diagrams - it gets a bit weird in the late evening, but it looks like you'd only need one more unit.)
If everything were 3-car, you'd only need 15 diagrams all day to run the Cross-City service (plus one extra unit in the morning for 2U10/2G10). In reality, there are 19 units out all day, with basically four diagrams running around all day as 6-car (though there is some swapping of pairings at Four Oaks). Two other units strengthen Cross-City services in the morning peak before switching to Wolves-Walsall runs.
So, either LM find one 350 from somewhere to replace a 323 on some more Wolves-Walsall runs, or one of the 6-car diagrams becomes 3-car to allow for the extensions to Bromsgrove. Not ideal, but could it be viable in the short term?
Since the journey to and from Bromsgrove only adds 20 minutes, only extending to Bromsgrove hourly requires sitting the unit at Bromsgrove for 40 minutes - and
still requires an extra unit over today's diagrams. So from the point of view of efficiency of rolling stock usage, it makes more sense to extend 3tph to Bromsgrove straight off.
That said, the crews who sign down to Bromsgrove may not currently be the same crews who sign 323s, so perhaps some time will be needed for route learning / traction learning to run the full service.