I leased a place a few years ago that had a concrete crossing very similar to the one in your second photo above. It wasn't as long as what you said you would need but it was wide enough for a semi and cattle trailer to cross. It had a longer approach slope than the photo on the upstream side and a normal flow would flow about three or four feet wide and few inches deep over the center of the crossing. During a flood it was the full width of the crossing and about three feet deep at the center. Not a lot of tree debris to deal with so upstream water traveled fast. The upstream edge of the crossing was probably about 18" thicker than the rest of the slab and it had a lot of salvaged sidewalk laid in at an angle to the stream. This let the water come up and over the crossing better than a vertical slab edge to go over. I think there were about four slabs in that angle and it was about twenty feet wider than the crossing drive lane. They did the same thing going downstream to prevent the water from cutting a big hole in the creek bed when it went over the drive lane of the crossing.
I also have a fairly large headgate structure on my current place and it has stacked sidewalk slabs for the walls and approach to the headgate and a lot of rip rap downstream. It has withstood highwater for about ten years without any erosion on the stream bed either up or down. The upstream ditch bed is level with the top of the stacked slabs and has a fair bit of large rock in it as it comes to the slabs. This ditch runs about six months a year and flows a lot of water. The depth going over the headgate is about two feet most of the time and a bit higher in heavy rains.
I don't know if this crossing would get any design help from your local Federal or State farm engineering sections but here is a bit about crossings showing some design criteria for what you are talking about doing. This link covers simple crossings up to multi culvert projects resembling a bridge.
https://www.fs.fed.us/t-d/pubs/pdf/LowWaterCrossings/Lo_pdf/6_Chapter5.pdf
