Finally had a chance to look over your answers, and see what new ideas they would spark.
37-down: シュクダイ. Having flashbacks of Endless Eight, here. I think I figured that when I first saw the clue, but the word just wasn’t coming to me.
31-across: No idea, but maybe アクイ
And done. Quick glance at the answers page for verification, and it looks like everything is correct.
I actually managed to work out a bunch through the middle of the puzzle, but I’ve left my book at home, so I can’t recall exactly what they were. 21-down is ハレースイセイ, and 18-across is アーク, but I’m fairly sure I had more than that…
Edit: Here we are:
13-across is スフレ (tentatively)
21-across is ハンシ
31-down is イズ
Wonder if I need to learn the lost art of typing the answers on the photo of the grid so I can post it here…
Yeah, I can’t figure out what both Hakodate and Nagasaki are famous for either. They are both major ports, but since みなと doesn’t fit, I wasn’t so sure. They also both suffered city-destroying fires - Hakodate in 1903 and Nagasaki in 1663 - but while かさい does fit, I’m not entirely certain that’s what the cities are famous for.
Nice. You know your botany.
So does “baby car” and “sports car”, is the logic. I’m… not sure how I failed to spot that. Maybe I did, except I tried to write it on the wrong space in the grid, so it didn’t fit.
Having スシ in 1-across has given me a brainwave for 1-down: it’s スイリョクハツデン. And 5-across is ハッポウスチロール. Then I guess 17-down is ファウル.
And with such long words on the grid, I’m pretty much gonna have to fill it in so everyone can see.
I had a sit-down to see what else I could hammer out, and wound up accidentally finishing the puzzle. I confess I don’t quite get the logic of one or two, but they fit, sooo…
In rough order of solving:
14-down キャンプ (and considering how much I love Yuru Camp, that should have sprung to mind sooner)
15-across ヤケイ (annoyingly, the fact that Hakodate is famous for it’s night views was mentioned in the Wikipedia article I was reading for research. Didn’t occur to me to check if Nagasaki was too)
10-down セッケン (Still not entirely sure what “paper soap” is). This automatically makes 4-across クセ and 6-across ツケ, and honestly, I don’t understand either of them.
25-down クチベタ, which makes 19-across ルイベ and 22-across セタイ.
28-across ヤスネ, which makes 27-down ランシャ
And left until last because I can’t really see how it fits the clue at all, 37-down ミネラルウォーター