Okay, Projects can't be hurried by whipping, cash or even a great Engineer, correct? However, excess hammers carry forward to your next build. So assume that you are going for a space race victory, and are about to begin the Apollo program. Is it best to:

1) put a minor unit/building before the Apollo Program in the queue and then hurry with a Great Engineer to get a massive overspend? Or will the excess hammers be lost?

2) Each turn, hurry a unit that requires a resource and then pillage your resource? Will that result in the build of a cheaper, earlier unit and so create excess hammers for the Project?

3) Something else that I haven't even considered?

Thanks. I've come across references to there being a maximum number of hammers you can overflow into the next build, but haven't seen any explanation of how that max is determined/what it is!

excess hammers will be lost...

Chop chop chop is basically the only way to go about it faster than normal... The pillage resource trick might work though, never tried it...

Yes overflow will go into projects.
But no, a GE will not give you any massive overflow. He will finish the building currently in progress but he will not give you more hammers than needed to finish the build.
When you loose a ressource needed to produce a unit, it is removed from the queue and you don't get the hammers back - those are not overflow, those are hammers you put in a build that can not be finished. I think you get some gold compensation there, not 100% sure however.

The maximum overflow is determined by the hammer cost of the build that overflew. So if you built something worth X hammers you can keep another X (or was it 2*X ? My memory is not what it once was...) in overflow. The rest will be compensated in gold.

And Lastly... If you use multiple turns to collect increasing overflow from stuff, why not just build the project in the first place. Might go faster that way.

Yeah, with ironworks, workshops and mining inc the projects are quite quick anyway.

When you get to the point of the game where you can build projects, there's no reason not to have a city which can build it under 10 turns anyway.

Whip and chop for overflow the turn before starting it and the excess should carry over right?

Yes, it will.
But do you really want to whip a size 20 prodcution city ? It will take ages to regrow...
Choping is also possible while building the project. If you (and the Lumberjack AI) didn't chop everything already...