I suggest you figure a different way, or rewire the jack. I've tried several bi-directional amplifiers in the past, and the results were very poor. There's simply no substitute for a good feed directly from the external cable connection.
I've seen asymmetrical 2:1 splitters that have a lower insertion loss for one leg than the other, which "might" help. OTOH, If you're so marginal that the splitter causes the problem, there's probably not much hope. Also, many 2:1 splitters have a much greater return loss than you can tolerate.
I've seen asymmetrical 2:1 splitters that have a lower insertion loss for one leg than the other, which "might" help. OTOH, If you're so marginal that the splitter causes the problem, there's probably not much hope. Also, many 2:1 splitters have a much greater return loss than you can tolerate.