Many ways to go about it for sure. I like the adding a 2nd 24" beside the first personally as it can actually be slightly higher and on a dry side 2 feet away only flowing water when the first is half full. I been contemplating replacing my bridge with a 36' or so culvert with creek run on top. My bridge has a good frame still but the treated wood deck and poles are shot. Cost wise the treated wood is about 1/2 cost of a culvert and I can place it dead onto the bedrock and back-fill with the wash/gravel out of the creek to a pretty deep depth if I want and can drag logs across then without worry about damaging the decking on the bridge.
On your 36" if you pull out the 24" try to maintain the half round bottom and build out for the longer length. Stake some rebar into ground & cheap rope over top. Bend a U on one end to tie rope to the rebar & dont hammer it all way in until the ropes are on it. Hammer rest of way down to tighten the rope, (assuming you are not on bedrock now.) Back fill right on top of the culvert then going slow but dont pack it tight to the culvert. It will tend to PUSH UP trying to pack it too tight real fast can still push them up if you are too far off the side of the culvert. It will naturally pack and silt in as the creek flows thru & some will go around it silting it tightly in no time.
This is what my creek bottom looks like flows 90% of time only been damp holes/springs/dry 3 or 4 times in 13 years but been no "Top Flow over gravel" usually less than a week or two per year & still flowing THRU the gravel.

creek here is about 6'wide with level-ish bottom with maybe 1" water flowing. I can drive my 6' box blade up/down the creek in some areas when it is low flow.
In Winter during snow melting time w frozen ground.
What the "Bed Rock" sandstone/shale rocks look like, this is about 3sq feet of rock and I've built 3 Patios out of it by removing it when the wash is dry.
This is what it looks like when we get 2"/hr rain all day...

I ended up having to move close to 80yards of gravel that washed into my park/picnic area after this flood, we ended up with 3 rains that have done this to me in 13 years now. Pic was taken from my Bridge I want to replace, there is a Granite Bolder where it is spreading left & right that is maybe 5'x4'x? I tried to move it once but just spun all 4 tires on my tractor. (busted a 5/16" chain then tried 3/8" chain when lost traction.

looking uphill same day as above pic.
Tried to find a pic of the bridge but it is not listed now, must have deleted it off PB... The above FLOOD is about 4' wide INSIDE the banks and maybe 16" deep on average at the center where it spread out was maybe 15' wide and turned left into the mowed grass picnic area. I had a gravel bank this time that was maybe 100' long by 4 or 5 feet wide and maybe 18" deep of wash/run gravel sand mix. It flooded that time and one more time the following week AFTER I cleaned it all up and re-seeded the picnic area ... Go figure it was just my luck lol.. My neighbor and I put it all into his drive using my tractor & dump trailer and he loaded the dump trailer. The last time it washed out I used larger rock to build up the bank in that area which I'm hoping will solve that.
Mark