I'm at max troop for my food. How do I get around that and get a stronger base?

If it is important to generate lots of food then you will need to increase production or reduce your troop numbers. Apart from upgrades you can increase production with some hero skills if you can recruit the right heroes.

However the game is considerate enough to not let you run out of resources, food (and fuel) has a cap that if you go below will stop feeding your troops (with no repercussions) and let you generate some. As you level up the cap level increases so you should always be able to keep a minimum level of food.

Depending on your level (it is easier when you reach higher levels) you can concentrate on earning reward chests that contain resource items. Complete daily challenge stages, clash of zones etc to get rewards) . The resource items you get from this are saved and can be used when you need them to top up for upgrades, research etc.