Yes, if you look at a map the shortest route is on the alignment through Bedford (which still exists) then bridge the Bedford bypass (road over) skirting by Willington (as it did) with a slight deviation around Blunham, cross the A1 (again road over) and you are in open country North of Sandy, with plenty of room for a flyover the ECML to the up and a chord from the down.
At Hitchin there is no reason why a cambridge bound service could not use the up platform and then reverse and utilise the old down Cambridge line, for West bound services it could utilise the flyover to access the down platform (I'm sure it's bi-directional) and again reverse to head North.