Larsenex makes the most important point. It doesn't really matter whether you prefer the combat aspect of 1UPT or Stacks (I prefer stacks but that is neither here nor there), but if a game mechanic can result in paralysed in-game movement then that mechanic is broken. The solutions appear to be relatively simple (in theory);
a) retain 1UPT but limit the number of units which can be produced, thus ensuring that there is always enough space to move or,
b) reintroduce stacks.
Now, I would favour the reintroduction of stacks, but it is more than possible to fix the 1UPT system with some form of production limit. What such a production limit should be is not something I really want to go into here, but it is perfectly possible and is the most pressing absolute necessity for an in-game fix. Limit production to ensure space and 1UPT will work (conceptually - the other problems with e.g AI usage are a different issue).
With regards to stacks - if stacking is to be used it must be unlimited otherwise the same problem as with 1UPT and space will have the potential to recur (and it may be much more difficult with e.g 6UPT, but theoretically it still exists). A solution to the unlimited and seemingly unending SoDs is, of course, a production limit.
When it comes to combat resolution, 1UPT is indeed intuitive and logical. But to make that work in a strategic sense we need to come back to [drumroll].... production limits. Because otherwise its back to the Carpet of Doom and all that entails.
Personally I would like to see some form of unlimited stacking for strategic movement, and 1UPT for combat resolution. However, this may involve other problems such as the creation of a tactical battle minimap, and might be something that players who care little for the combat aspect of Civ find irritating or distracting.
To conclude, I think its probably fair to say that I don't know the optimal answer. But I'm fairly sure I can see the problem...
Oh, and if 1UPT is to be retained please, please, please introduce a mechanic which allows me to brigade units for mass strategic movement. As it is there's just too much click, click, click just moving around the map.