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I did my first piece of touring last month. A three week trip. I feel like we neither coasted nor pushed ourselves. A nice middleground, considering we were hauling some 15 kg per person, are in pretty bad shape and just wanted to take in the sights.
We did around 60km a day, usually starting a little after 9 in the morning and arriving at between 5 and 7 PM.
Google Maps with the bike setting counts on about 16 km/h. At the end of the day we had usually done about 10km/h, if including breaks in the equation.
In short, I wouldn't try 250 km in one day. Two long days, minimum.
For me atleast, the limiting factor wasn't physical exertion, it was the slowest guy in the group and the amount of daylight hours available - hope you're early birds. Or that sunset comes late. If your bikes are poorly fitted or you're wearing inappropriate clothing, pain will be a factor. Bib shorts with nothing underneath is advisable (probably a must) but it's a big expense for a one-off trip, although you may become smitten with cycling, as I kinda did.
Do you have bikes? What are you open to buying/spending? Have racks, panniers?
If you're sticking close to civilization, a halfliter waterbottle ought to be enough, if temperatures are reasonable. Try to cut the weight but don't be obsessive about it. A few extra kilos on a bike aren't nearly as devastating as when you're hiking (meaning, bring your tent if it's reasonably lightweight - building a shelter isn't always viable, I'd imagine that's certainly the case on a salt flat). With cold temp, ears, lower arms and lower back were frequently the problem areas for me - put on your intended clothing and sit on the bike, note how your wrists and lower back are exposed. Cycling-specific clothing is made with this in mind however.
Our chains would go 400-500 km inbetween needing a lube-up iirc, so if you lube up before leaving you might not have to deal with the squeaks.
