Just needs a longer run up
It's always easy to criticise on this sort of thing, but the speeds & times quoted suggest that acceleration rates & available track length are both significant issues if the design stats and quoted figures are to be believed.
Considering only aerodynamic drag, the power increase required to boost max speed from the old record of 127 to 139mph is 'only' around 30%, but the quoted theoretical max speed of 170mph would suggest the car should be capable of producing around 2.5 times as much power as the Stanley Steamer (and anyway 268kW of power should be sufficient to power a low drag vehicle to these kind of speeds without difficulty).
This would suggest either a big shortfall in power (by around 80%, which seems unlikely) from that predicted, or a large calculation error in another area (e.g. drag coefficient, again unlikely), or simply that the car does not accelerate quickly enough to get close to its theoretical Vmax in the time/distance/fuel/water/whatever available.
If it takes 2.5miles to get up to speed (presume he means 140mph), then the *average* acceleration rate is a fairly unexciting 0.5m/s^2, and if that accel rate could be maintained (optimistic) it would need another 2km to get up to 170mph. Assuming it can carry enough fuel for a longer run then the simplest solution would be to go somewhere bigger, hence salt flats are a popular venue, but running on salt can bring further issues with stabilty, rolling resistance etc.
Other than that, the fundamental options remaining would be to a) reduce drag - although we should assume that it's at least 90% optimised, b) reduce weight, although again a 10% improvement would probably be good going, or c) add more power, which would probably come at the expense of adding more weight, not least from the water required.
Apologies for the gratuitous mixing of units!