From looking at the current diagrams, there are 23 diagrams for the 26 LM 323s, with three spare units. There are indeed 14 all-day diagrams on the Cross-City, of which three are 6-car all day, so that's 17 units.
Two of the Cross-City diagrams are 6-car in the morning peak, but each have one unit split off to form Walsall-Wolverhampton diagrams (one from about 9am, one goes back to Soho at 11am and comes out again at 3pm). There are two units on Walsall-Wolverhampton all day, and another which comes out in both peaks (the last covers the oddball Wolves-Four Oaks in the morning). The final unit shuttles between New Street and International, and that's all 23.
That means that at least some of three of the five Walsall-Wolverhampton diagrams must be formed of 350s - one until 3pm, one in the morning peak and one most of the day from 8am to about 5pm.
As I understand it, the 10 new 350/3s are logically split as 7 for improved fast services to Northampton in the peaks, and 3 for the West Midlands, which I believe means replacing *all* the 323s that currently do Wolves-Walsall with 350s. With a little rejigging of the diagrams, I suspect that leaves you five 323s spare - and five 323s is exactly how many you need, I believe, to run the 3tph to Bromsgrove / 3tph to Redditch which is planned.