A 4th option might be to get a sound card with a higher sample rate? (although you'd need to confirm that your sound card has at least three actual ADCs, rather than mixing inputs into two).
(My elderly UA-101 is good for 24 bit 192Ksa/s, with 20Hz-40KHz analogue paths. I hope things have only got better in the last decade).
Is your team better at hardware or software?
Edit: Nanosecond measurements? That seems ambitious and possibly unnecessary. 1500m/s suggests that 1mm resolution is 2/3 us, and you're not seriously hoping for 1mm, are you? Where on the wave are you planning to take your 'distance' point? If your transducers are at all resonant, there'll be a slope from 'no sound' to 'sound'.
Edit2: I think that, whatever solution you pick, ease of prototyping, debugging and changing things trumps pretty much any other requirement. Do you have scope plots of what the current system sees?