Grammatically correct way to use the word sensei

The way it's used in Japanese, it's always after. Might as well do it that way. Japanese doesn't have capitalization, but I'd say capitalize it by analogy with Professor in titles.

In Japanese it comes after the name, for sure. You can also use it as a standalone title.

I don't know what the style guides say, but my inclination would be to capitalize it when used as a title or form of address, since we capitalize titles like "Mister" and "Doctor."

Basically, +1 to everything morngnstar said.

When I hear the word used in martial arts circles, it's most often as a standalone word. It's almost always used this way. When a name must be used, the name comes first.

For what it's worth, the usage I typically see is hyphenated (i.e., Kanekoto-sensei). That said, if the characters in question are not familiar with Japanese language, like if they're all Westerners at a dojo, "Sensei Kanekoto" would seem the more normal use to me (as that's how things were at my Korean dojang.)

Unless you're setting the narration up as an outsider's point of view, I would stick with Kanekoto-sensei. In the context of a samurai story, 'Sensei Kanekoto' would strike me as odd. (Though I am a bit of a Japanese nerd, so my experience may not reflect your targeted audience.)

I'd say definitely do it the Japanese way in that situation.

I can't say I've ever seen it used before a name, but I've never seen it used by anyone who isn't at least a little familiar with the Japanese language and/or addressing a Japanese person. As far as I'm aware, the term "sensei" when attached to a name is always a suffix, never a prefix. It'd be like calling someone Smith Mr. in English.

It can be used as a standalone term (e.g. the same way we'd say "Professor, I don't understand this!" or "Doctor, I need help!" in which case it should likely be capitalized) but if you're using it with a name and especially if the the narrator and/or addressee is Japanese, then stick with adding it as a -sensei suffix.

Isn't sensei an honorific? Kanekoto-san, Kanekoto-sensei?

In my ikebana class, the teachers referred to themselves and each other as "[name]-sensei." Though I guess you can't really tell if a name is hyphenated when spoken aloud...

When I took Aikido for a couple years, we used <name>-sensei (as a honorific) when talking about a specific instructor in the third person and Sensei when addressing the instructor directly or when there was only one person we could logically be talking about. It was one of very few Japanese conventions we used regularly (we didn't call other students sempai or count out excercises in Japanese for example). So even in a western setting, the Japanese-way is most likely correct here. (Note that both instructors did train under a Japanese teacher.)

Coming in late to this, but what we have picked up as we study Japanese language and art both in use/observation and from translators and teachers is when used with a name, sensei follows the name. So it is always [Name] sensei (always lowercase, capitalization of the title seems to be a Western thing). Usually with a last name, although sometimes with the given name. The Sensei [Name] form is something we've only seen in Western culture, usually in martial arts.
Sensei may also be used as a stand alone address, similar to doctor or professor. In this case, I would follow normal capitalization rules simply for clarity and continuity in the manuscript (although in Japan, there would be no capitalization of the term).

As for whether or not to use the Western approach of Sensei [Name]: what would your character use?
If your character uses sensei because they have studied martial arts in a Western setting, it's likely they would use Sensei [Name].
If, however, they lived and studied in Japan, they would likely have adopted the [Name] sensei style because that's what they heard/used there.

Whether or not your readers will know the difference is a completely different subject. Some will, some won't.

ETA:
For what it's worth, we use [Name] sensei both in written and spoken form when talking to or about our teacher. We rarely say "Sensei said..." It's usually "Naka sensei said..."

Funny, I had some long and intensive training in martial arts, but we had no sensei, at least in an official sense. Our instructor was in Special Forces, and we just called him by his name.

Anyway, how the word is used in fiction would depend on the character using it. Name first is correct, but many characters might not know this, and would have to be corrected.

I would agree with using Blinkk-sensei in narration if that's the way it's being used in dialogue.

This is not based on any particular knowledge of martial arts or Japanese grammar (though I can ask for a cup of tea and a complete sashimi meal, which I am disproportionately proud of), but because switching between one way round and the other way round seems like it will distract the reader and mess with the flow.

You don't want readers puzzling over the very question we're puzzling over in this thread, you want them to focus on the story, and keeping it consistent seems the best way to achieve that.