If you get Hiawatha in a random civilization then build them. Once you get longhouses you can really get that extra hammer per lumber mill. If you have more lumber mills, they can really add up for production... make sure you have a good flood source somewhere though.
The food problem from Forest start as them can often be solved by playing with Legendary starts so you have more bonus resources. The AIs also get this, so it's not cheating.
Found a religion and select Feed the world for an extra 2 food per city. (If you've gone tradition, this is even more due to bonuses for surplus)
If coastal, then food cargo ships.
And if all else fails and you still need more food, then the same rule about what to do with too much Jungle rule applies: It's the fresh water forest that's more expendable.