The Bedford & Cambridge pair are a similar distance from Birmingham as Oxford & Reading.
That's not correct. As pointed out above, Reading is nearer to Birmingham than Cambridge. Also Oxford (67 miles via Solihull or 72 miles via Coventry) is nearer than Bedford (83 miles).
The populations are very different.
Reading+Oxford 375k
Cambridge+Bedford 250k
Furthermore, comparing entrances and exits:
Reading+Oxford 20.3m
Cambridge+Bedford 13.3m
Bedford-Birmingham is a journey that can already be made now. We can see the numbers:
Bedford-Birmingham New Street 2961
Bedford-Birmingham International 243
Bedford-Coventry 786
Total 3990
And even looking at the pre-pandemic numbers we have
Bedford-Birmingham New Street 5431
Bedford-Birmingham International 712
Bedford-Coventry 1865
Total 8008
Your calculation relies on Bedford contributing more than 70k journeys, clearly that's absurd.
I think we can disregard the contribution from Bedford here. When East West Rail opens the new destinations for 70k journeys to and from Bedford will be Oxford and Cambridge, not Coventry and Birmingham.
I take your point with regard to Cambridge-Coventry/Birmingham International. Using the Reading comparison, adding Coventry and Birmingham International to my Cambridge-Birmingham New Street 25k estimate would get the figure up to about 35k.
It is still a small number.