I have a complete small toolbox which I use for circumstances like this. Check it with the airlines. I've taken it on domestic and international flights, no problem at all.
i wouldn't bother with the fluids until I got there. Easy to obtain at auto parts stores.

When I did this with my daugther (Denver to LA) I took the train for the adventure (bought a 409d). Amtrak does run across the southern part of the US.

Twice I've flown to pick up a vehicle and walked away from it. I always buy return tickets now with the return flight the following day.

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1977 300d 70k--sold 08
1985 300TD 185k+
1984 307d 126k--sold 8/03
1985 409d 65k--sold 06
1984 300SD 315k--daughter's car
1979 300SD 122k--sold 2/11
1999 Fuso FG Expedition Camper
1993 GMC Sierra 6.5 TD 4x4
1982 Bluebird Wanderlodge CAT 3208--Sold 2/13