I don't have a solution, but I do have a suggestion.
Have you tried saving your current game, swapping some of the units_32 picture positions by using cut 'n paste, then reloading the saved game?
Because this is only an animation change and not a rule change (i.e., Civ3 ends up with the same file names it started with) it should be possible to make such changes within a saved game without crashing it.
This may help to find out why the game is choosing certain units_32 pictures instead of the correct ones.
(I have only just downloaded 1.29f, and so I'm a long long way from the modern age, as well as being far too busy creating new units to try this myself at the moment. But I would like to know the outcome).
LATER EDIT:-
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Ah! I think I've sussed it!
Zulu9812 - in your units_32.pcx file, the 8 era dependant pictures (i.e. the 3 leaders, 3 armies, and the modern settler & worker) have been moved to the very last squares. But it's my understanding that since the 1.21f patch this is no longer neccessary. These 8 pictures should be LEFT IN THEIR ORIGINAL POSITIONS, which is straight after the F-15 & Privateer pictures, and all new unit icons should be placed AFTER them.
If you use the save/cut 'n paste/reload method I suggested above, then you should be able to fix things without (...hopfully!...) losing or restarting your current game.
Please let us know if this works
