Thanks a lot, pocketmofo. I'm keeping a notebook and I have a page of all your suggestions and notes, so it helps me out later when I need it.
Updated the front page with all I've done so far.
Here's a tricky one for me, a conversation between Kawachi and Kanmuri:
RAW Page
Kawachi: ところでや、冠。
Kawachi: tokorode ya, kanmuri.
Kawachi: By the way, Kanmuri.
Kawachi: そもそもワイらは信濃町の特産物について、なんも知らんワケやが...
Kawachi: somosomo waira wa shinanomachi no tokusanbutsu ni tsuite, nan mo shiran wake ya ga...
Kawachi:
Couldn't really get it: At first we [Shinanomachi's specialty product]
Kawachi: あの堤っちゅう男に勝つためにも、まずそこらへんから教えてもらえんか?
Kawachi: ano tsutsumicchuu otoko ni katsu tameni mo, mazo sokara oshietemorae n ka?
Kawachi: That guy Tsutsumi, he wants to win too, so shouldn't we get someone around here to teach us?
Pretty sure that's not right, but it was the best I could guess.
Kanmuri: ああ、いいですよ。
Kanmuri: aa, ii desu yo.
Kanmuri: Yeah, it's fine.
And this I think I got right, but if someone could check:
Kanmuri: 信濃町で勇名な特産物というと、とうもろこし、りんご、フルーツトマト...といろいろあるワケですが、
Kanmuri: shinanomachi de yuumei na tokusanbutsu toiu to, toumorokoshi, ringo, furu-tsu tomato... to iroiro aru wake desuga,
Kanmuri: When you mention specialty products from Shinanomachi, there's sweet corn, apples, fruit tomatos... and various other items,
Kanmuri: ジャムにするならやっばり
Kanmuri: jamu ni suru nara yabbiri
Kanmuri: but if we're going to make jam,
Kanmuri: ルバーブでしょうね。
Kanmuri: ruba-bu deshou ne.
Kanmuri: then it should be rhubarb, right?
Azuma: ルバーブ?
Azuma: ruba-bu?
Azuma: Rhubarb?
Kawachi: なんやそれ?
Kawachi: nan ya sore?
Kawachi: What's that?
Kanmuri: 欧米でよくジャムとして使われる甘酢っぱい植物のコトです。
Kanmuri: oubei de yoku jamu toshite tsukawareru amazubbai shokubutsu no koto desu.
Kanmuri: Westerners often used sweet vinegar in order to get jam from plants.
Kanmuri: 日本では古来より大黄と呼ばれ、漢方薬として使われていたモノなのですが...
Kanmuri: nippon de wa korai yari daiou to yobare, kanpouyaku toshite tsukawareteita mon nano desu ga...
Kanmuri: In ancient Japan it was called "daiou", used as an herbal medicine, but...
[Note] - Daiou is written with the words for "big" and "yellow".