What is a good modification of rules to make a game of Dominion slower?
Things that require no actual house rules:

1. Get and use the Prosperity expansion (or the Dominion Base Cards set), and play more games with Colonies/Platinum.

Games with Colonies usually last longer, because it is not often worth buying Provinces. Instead of trying to get to $8 for Provinces, you are trying to get to $11 for Colonies.

2. Use setups that create longer games.

Some setups make the game go longer than others. Games with attacks will last longer on average than games without attacks. Games with more powerful cards like Wharf or cards that gain more cards like Workshop will be shorter on average.

Cards like Philosopher's Stone (from Alchemy), and Counting House (from Prosperity) become better in longer games. Any cards that give out Curses usually make the game go longer, because people's decks will be clogged. Strong trashing cards like Chapel will usually make the game go much faster.

Finally, alternate VP cards like Vineyards (from Alchemy), Duke (from Intrigue), Gardens (from Dominion), and Silk Road (from Hinterlands) can make the game go much longer, because one player can ignore Provinces completely and go for points with those cards instead (if the rest of the setup makes that a viable strategy). It takes 1 person a very long time to drain the entire Province pile, so if (in a 2 player game) 1 player is avoiding Provinces completely, he can make the game go long enough that his Vineyards and Dukes will be worth more than the Provinces that the other play managed to get.



I have not personally tried either of the following (as I prefer to play multiple faster games than fewer slower games), but a couple ideas that come to mind:

3. Increase the number of Provinces available.

If playing 2 player, you can use all 12 instead of 8. For 3 or 4 player, you could use 15 or 16. Either take the extra cards from the Intrigue set if you have it; or just use blanks or unused cards as proxies. The biggest issue here is that players will need to learn to not start buying Provinces as early as normal. If they start buying Provinces as soon as they hit $8, then the first 8 Provinces may be bought up, but then it may become unlikely to ever be able to buy the last few because your decks are clogged. This will also not make any difference for some setups.

4. Increase the cost of Provinces, like you suggested.

You do have to be careful with this, because in certain setups it can be literally impossible to ever reach certain amounts on a given turn; like if there's no way to increase your handsize. This will also not make any difference for some setups.