There was a post before that linked to a site where someone did some asymptotics on VP gaining. I think it was in the thread about determining Engine vs. Non-Engine. I think the jist of it was that Big Money accumulated VP at a linear rate, while Engines can accumulate at a superlinear rate. I think good strategies could get to quadratic.
Big Money is linear, though it isn't the best linear strategy. (4 Princes of Monuments is 10VP/turn to BM's 3VP/turn, for instance, while a 95% reliable engine with 10 Monuments as payload and not greening is 9.5VP/turn).
Alt-VP is generally quadratic - e.g. a Prince of Ironworks gaining a Gardens and buying a Copper gains 1 Gardens/turn and increases the value of each Gardens by 0.2 VP/turn, for 0.2n^2 + smaller terms VP, where n is the current turn. (But even the Money/Gardens strategy of buying Copper on 0-2, Silver on 3, Gardens on 4+ is quadratic, just a lot slower).
Engines are generally exponential, at least in terms of greening power: to take the extreme example, once you've trashed your starting cards and gained 8 Highways, a Highway-Market Square deck doubles the number of Market Squares in it, so having megaturn potential that grows like 2^n. But after the megaturn it'll stall horribly and be overtaken by the Big Money tortoise. If, as stated in the OP, the piles are very large but finite, then this is probably the best. If the piles are infinite, then it gets crushed.
A more traditional engine (with some +Buy) will also grow exponentially, but again if you start greening in the normal manner then you'll splutter a bit before choking entirely. However, it should be possible to build an engine that can increase in size exponentially and also gain green exponentially (with a smaller exponent) whilst still being able to reliably draw itself.
Better than that, though, would be the engine with Goons as payload, which also grows exponentially and gains VP exponentially, but has much less to choke on.
Now I've written this, I realise it's essentially what that article said, I think, though I can't find it either.
[lastly: no, florrat isn't right, because Dominion involves shuffling].
Although the thing I like most about this solution is that it's constructable with straight edge and compass - interesting the different attitudes.