BRU seems to be the preferred connecting point within the LH group for all flights from the British regional airports to Europe and the US/Canada
Can't confirm this for BHX at all. Here, LH sends us through their primary hubs, FRA, MUC and ZRH. Despite BRU being smaller, I found changing from Schengen to Non-Schengen via the tunnel isn't great, not really better than FRA. Also, e.g. going BHX-GVA with LH and partners, BRU is more expensive than ZRH. SN has a patchy reputation I think in the UK, and the Avro isn't everybody's favourite aircraft.
On another point, I hope LH will not shift BHX-FRA and MAN-FRA to BMI unless they work on their flight experience. Have heard in various media that BMI's interior is a bit poor, as well as non-perfect in-flight service - LH customers are pretty demanding. Such a shift could be good news though for BE esp if they can put a E175 on the FRA routes. If both are jets, then I'd find it hard to pay extra to use British Midland instead of British European. I noticed though that LH has changed their age-old BHX flight numbers from 49xx to 9xx, which is probably a hint at a change. DUS would still be LH (Eurowings), that would then be the only German jet at BHX.