I don't know how "pretty" it needs to be when its done but rough cuts can easily be done with a chainsaw or a reciprocating saw with a long enough blade. A quick search shows blades that are 10" long which might be enough for the reciprocating saw. A 12" pruning blade like this bad boy from Amazon for example.
Might not be the best example but as long as the gullets are deep enough ( they would need to be for this. ) it should work.
Making wedges from the sides until there is enough room to work the tool though the 6" region.
Need to be really careful using the chainsaw. Very dangerous tool. Especially for the stance you might need to make this cut.
If you had an old style enormous hand saw for ripping the tie I imagine that would work as well as seen in this blog
Coming at it from the side with a broad axe would work as well. In the same vein as how logs are rough shaped into timber. You could also cut vertically down was a saw (hand or powered) several times across the length of the seat and pop out the waste with a large timber chisel or slick.
Much like I said in my comment those ties are commonly treated with creosote which is a known skin irritant amongst other health concerns like causing chemical burns. While you might be avoiding exposure by sealing it I will still mention this because the risk is there while processing the tie as well
(sawdust and what not.). Even if no one sits on it. Your skin and lungs are not worth it.