I was thinking about a hole saw attachment, however I do not think this will extract the wood if the depth does not exceed the total depth of the sleeper.
That's correct, and in addition you could easily find it nearly impossible to withdraw the hole saw from the wood (for the same reason that it can be difficult to remove the plug from a hole saw when it is used to cut through a board).
Probably the ideal tool for this is a Forstner bit (or saw-tooth bit, similar to a Forstner and often mistaken for one):
Source: About Forstner/Saw Tooth Bits on Lee Valley.
There are two buts though, and unfortunately they're both biggies.
The first is a safety issue: in general Forstner bits (and bits of a similar design) are not intended to be used freehand, but instead with a drill mounted in a drill stand, or in a drill press/pillar drill. Although many people do use them freehand chucked up in their power drills this is not good practice and the manufacturers of the bits themselves will often warn against it — "For use in a drill press only" or words to that effect. The greater the diameter of the bit the more caution you want to take on this front, and 64mm is a very large bit.
The second is that a 60-70mm Forstner bit is fairly specialised and as such is not cheap. Expect to pay around $50 or the equivalent for a good one.