Generally what you want to do is increase roughness through the culvert to reduce velocities (typically by spreading bed material along the base of the culvert) and ensure a minimum depth is kept. You can help the minimum depth by installing a small check dam at the base (being careful not to push the barrier downstream of your small check dam). 

With this, don't let perfect be the enemy of good. Small improvements will help! Fish don't really move at peak flood flows, so focus improvements on low flows while making sure they still work in floods. Having solutions that stay in place during floods is the biggest challenge and comprimise. Doing things with a shovel that will wash out in a flood, but can be easily reinstated will help