Origin of the word 床屋?

Question

Why is the kanji 床 (floor) used to talk about a barbershop?

According to some answers in the post linked in the comments, here's two possible explanations.

1. Originally barbershop had tatamis (this isn't really thorough, many places had tatamis).
2. Quoting: "There was a barbershop in the Edo period that had a tokonoma; people referred to it as 「床の間のある店」(the shop with the tokonoma)". This is also a possible explanation.

Maybe an expert in history and linguistics can pinpoint references of the origin of this word?

Answer 1

Origin of the word 床屋?
Why is the kanji 床 (floor) used to talk about a barbershop?

According to 語源由来辞典:

髪結いは、橋詰めや辻などに移動可能な店を出店したり、住居とは別に商売をするためだけに構えられた店で営業が行われていた。このような形式で営業している店は、簡易な「床」を設けていたことから「床店（とこみせ）」と呼ばれた。

髪結い used to work at mobile stores, or at stores separate from their home. And these kinds of stores were called [床店]{とこみせ} because they had simple [床]{とこ} (bed/bedding).

(床 can mean [床]{ゆか} "floor" and also [床]{とこ} "bed/bedding".)

デジタル大辞泉 also says:

とこ‐や【床屋】 の解説
《江戸時代、髪結いが床店 (とこみせ) で仕事をしていたところから》髪結い床。また、理髪店。

It was called [床屋]{とこや} because 髪結い worked at [床店]{とこみせ}. And according to the dictionary:

とこ‐みせ【床店／床見世】 の解説
商品を売るだけで人の住まない店。また、移動できる小さい店。屋台店。

[床店]{とこみせ} is a store that's used only for business and no one lives in, or a small mobile store, stall or booth.