Every so often, you discover almost by accident a strategy that seems to stand no chance, but in practice works very well. This is one such strategy, and here is how it works:
1. Buy IGGs, as many as you can, as often as you can.
2. Once they are gone, use all the copper to buy some gold.
3. As soon as you can, stock up on GMs.
4. Profit.
The key to this working is to hit hard and fast with the IGGs. Even if they scramble for duchies, an effective attack will prevent the duchies from running out before you can use GMs to empty the provinces (or hopefully, colonies). That means skipping on some golds during the midgame even when you hit $6. Half-measures won't work; this really is an all-in strategy. And don't forget that even though IGGs are only worth $1, they can be in play when you buy a GM. Every coin adds up here.
There are two reasons why this can fail unless the conditions are just right. First, if the $4-and-below cards are reasonably strong, if there are any trashing cards (even Trade Route), or if your opponents get even some of the IGGs, then they can just duchy-rush before you get more than a couple GMs, if that. The second reason is that
IGGs and GMs do not like each other. Most likely, your opponent or opponents would have to be in a coma for this to actually work. Happy April Fool's Day! (Now go gain a curse if you actually fell for this. :p)