How can I remedy a septic system that is sometimes below the surrounding water level?
You have the wrong type of drainfield. 

When there is a high watertable, alternate types of septic systems need to be installed, including: 1) curtain drains around your septic system (if the curtain drain can be discharged in a creek, swale, etc.), or 2) above ground septic system. 

1)  Remember, most drain fields are not designed to allow water to drain down into the ground, but rather allow the water to evaporate. (That’s why the drain line is laid fairly close to the ground surface...18” - 24”, rather than 8’ down.) However, a careful evaluation of the soil (perk test) and the topography of the site. 

Here’s a site that explains it pretty good. https://buildingadvisor.com/buying-land/septic-systems/how-a-septic-system-works/ 

2) Above ground systems rely 100% for the aeration of the water and the water is pumped up to it from the tank. They are expensive and seldom used. Usually, it’s just cheaper to pump after heavy rain storms that raise the watertable.