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Am I right in thinking that a London Midland Super Off Peak single Birmingham New Street to Euston is valid on the 1554 service and then next on the 1954 and is not service specific?
The last valid departure from New Street is the 1614 to Coventry, connecting onto the 1700 at Coventry, even though the train originated at an invalid time from New Street. It would not be valid if you started at New Street on that train at 1633.
After the evening peak, the first valid departure is the 1933 to Northampton, but there is no time advantage compared to taking the 1954.