Given that all those private keys were generated by the same person/people, there is a slight possibility that a pattern of some sort does exist tho that's pretty unlikely, given that someone has already managed to break #125 it means one of two things:

1- Somebody managed to find a pattern somewhere that reduces the search range by A LOT.
2- A large corporation invested some serious money in a few thousand GPUs and people like OP stand no chance of finding those keys first.

I think the second point makes more sense, having access to a truckload of GPUs and a better-modified code is probably what those folks are doing, it looks like the same person has solved both #120 and #125, so they are up for something, the "difficulty" of the puzzle has hit the ceiling now and the small guys have little to no chance in it IMO.

Also, I am not sure why OP wants to use an ASIC miner to brute force a private key, it makes no sense.