Depending upon the route E-W rail takes at Sandy, the station may need a total rebuild anyway
I'd expect a solution something like Nuneaton - where the Birmingham - Leicester line was put on a flyover over the WCML and onto two new platforms - that is the most likely scenario and minimises disruption to the ECML.
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Do you make up all of your "facts"?
Firstly the suggesed route via Luton does not go to Bedford. It's bletchley, Milbrook, new chord to MML, Luton, Stevenage, etc.
You claim Bedford, Hitchin Cmabridge would take 45 mins. You then claim thats longer than the X5 bus takes. The X5 takes 75 mins from Bedford to Cambridge. Last time I checked 75 is greater than 45 not less. So a train via Hitchin would still be much faster than the X5 bus.
There was no clear direction on whether a via Luton route would or wouldn't include Bedford. Pretty much everything published about EWR included Bedford - either way you'd still only be saving 5 or so mins if you pathed in south of Bedford via a new chord AND you'd lose any business from Bedford unless you built another new station. Not to mention the challenge that the MML from Bedford - St P is pretty much at capacity now, so the opportunities for non-stop high speed running along that stretch are limited without relieving either EMT or Thameslink of one of their paths. So I maintain you'd be looking at a journey time of circa 20 mins Bedford - Luton and probably 20 mins Luton - Stevenage.
On the Hitchin option - factor in you'd need a reversal at Hitchin to make that work OR another flyover to allow direct access to the Cambridge line and avoid Hitchin - so once again losing connectivity.
The fastest you'd be able to make Hitchin - Cambridge is 25 mins - take a look at the current services and the fastest is 33 mins which includes stops at Letchworth, Baldock & Royston. There are limited options to run fast from Hitchin to Cambridge - again the line is close to capacity - but lets assume there is a small amount of journey time improvement possible.
Again, Bedford - Hitchin is about 20 miles, so practically you'll struggle to get that much below 20 mins journey time. So 45 mins to cover Bedford - Hitchin - Cambridge is absolutely best case.
On the X5 - my mistake, I'm sure when I'd previously checked it wasn't that long.