At the summit, a cutting at Kilsby would have needed to have been 120ft deep (Tring cutting is only a third of that). That's well past the point at which tunneling is the cheaper option. That's why Stephenson went for it.
His problem was that there was a layer of quicksand that didn't show up in the test bores. Whether he didn't know or ignored warnings is a moot point. I live only a couple of miles from Kilsby and that quicksand has been known about for generations. The previous canal builders were certainly aware of it as they changed plans to avoid it. There are also records of Stephenson being warned about it by Dr Anrold, the Head of Rugby School.
The tunnel was indeed late (although even so only took three years to construct) and well over budget. The original contract to a J Nowell & Sons was for £99,000 (that's around £11.3 million today). They gave up after a year, the railway company taking it on themselves. It eventually cost £320,000 (£37 million).
As an aside, although the tunnel itself was not affected by landowner objections, the route through Rugby was. The original plan was to run slightly south of the present approach from Weedon, which would not have required an embankment, then curve left and run south of the town centre and Rugby School, rejoining the eventually built line at Long Lawford. Rugby School thought that a bit close and objected - and they had clout!
As for the huge air vents, they were apparently a response to worries about people in trains suffocating. A local story tells how three drunken navvies plunged to their depths one night when attempting to jump one of the then unprotected openings.
I suggest anyone interested in Kilsby (or indeed any of the history of the London-Birmingham line) takes a look at 'The Train Now Departing: Notes and Extracts on the History of the London and Birmingham Railway' on the the Tring Local History page -
https://tringlocalhistory.org.uk/Railway/index.htm. Chapter 7 deals with Camden-Cheddington, Chapter 8 Cheddington-Birmingham and Chapter 9 the Euston extension.