That is a tough bi-district draw in terms of travel! While I am not sure of the situation in regards to money (basically can you afford to play on a 11-man field,) Eden looks like the obvious choice in terms of sixman schools half away between Evant and Nueces Canyon.
You probably would not be posting if that was a good option, however, so here are some ideas as someone has lived near both places and is an zealous sixman football fan.
1. Pick a school close to Eden: I think Lohn would be an excellent and cheap choice; they have really done a nice job revamping their field and I bet Leon Freeman would jump for joy if someone asked to play a playoff game there. I am not 100% sure if it could seat enough people, however. I think it is slightly closer to Evant, but you could ask for it in a coin toss. Panther Creek and Paint Rock would also be in consideration. Maybe Veribest? It is probably too far to the west anyways, and I hate their field because you have (or at least in my day) to take a bus from their field house to the football field.
2. Play at a private school in San Antonio: Although the distance is pretty even, I am not sure about pricing or anything like that. I also would think the Nueces Canyon people (coaches, fans, players) would be more familiar with it since more Evant people probably go shopping in Austin or even DFW.
3. Prairie Lea: This is an interesting choice because they are in Nueces' district which would, at least in theory, give them familiarity but is quite a bit closer to Evant. I saw their field once and suspect they would agree to host it at a cheap price. While I doubt this is a legit choice, I thought it was an interesting idea.
4. Flip home and home OR something like Lometa against Leakey or Medina: This is always an option obviously; I would do it a lot if I coached Sanderson, Dell City, High Island, Medina, Leakey, Nucese Canyon, or another school far from the rest of the sixman community.
These are just ideas as I have lived in Lohn, Marble Falls, Ranger, Cleburne, San Marcos, and other towns in the area. Whatever you decide, I wish you the best of luck, coach!