Thank you charghwI', voragh, SuStel, and nIqolay Q for sharing your thoughts. Comments on specific parts of your messages follow.

charghwI':
> Meanwhile, going back to the original, I think this is a weird use of the English word “especially”.
SuStel:
> Yes, it is neither clear nor specific.

True, the original sentence is unclear and unspecific. I remember that the need for expressing "especially" came when I saw a sentence saying something like:

"This god was especially a god of .."

And I couldn't quite understand what the actual meaning was. So the need came to find a way to express "especially" in the same unclear and unspecific way. I thought "if the original is unclear, then the translation should be unclear too". So I said to myself "translate it in a similar unclear way, and good luck to the reader figuring out what the actual meaning is; as if anyone is ever going to read the klingon translation anyway..".

So I did it using the {-chu'}, in a manner similar to the sentence that I wrote in the initial post:

"he is a god of rain, thunder, and especially hurricanes"
{SISmoH tuDmoH 'ej vungmoHchu' Qunvam}

But reading the various replies of this thread, I was happy to see that there are many more options.

voragh:
> nov nuH 'oH thalaron woj'e';  lulo’qu’ rIymuSnganpu’.
> Thalaron radiation is an alien weapon; the Remans use it a lot.

Indeed, I could use the {-qu'} too: {SISmoH tuDmoH 'ej vungmoHqu' Qunvam}

voragh:
> nov nuH 'oH thalaron woj'e'. pIj (nuHvam) lulo’ rIymuSnganpu’’e’.
> Thalaron radiation is an alien weapon.  The Remans use it (this weapon) frequently.

I hadn't thought the possibility of using an adverb, but indeed an adverb could work too: {SISmoH tuDmoH 'ej roD vungmoH Qunvam}

charghwI':
> I think more along the lines of {tlhInganpu’ qu’ law’ Hoch qu’ puS} or {tlheylaran Qob law’ Hoch Qob puS}.
> In other words “especially” suggests “uniquely” or “to an extreme degree that is unique’. It’s special because it is extreme.

Using the law'/puS construction is another wonderful idea, which didn't cross my mind. So, I could write:

{SISmoHlaH tuDmoHlaH 'ej vungmoHlaH Qunvam, 'ej laHDaj wejDIch potlh law' Hoch potlh puS}

nIqolay Q:
> nov nuH 'oH thalaron woj'e', lulo' rIymuSnganpu''e'.
> "Thalaron radiation is an alien weapon, Remans in particular use it."

I think that at some point the thought of using the {-'e'} did cross my mind, but I got the feeling that if I used the {-'e'} this way, perhaps the meaning would become that "of all the alien races, it is only the remans who use the weapon". But I understand now that this would be the case only if we wrote {nov nuH 'oH thalaron woj'e', lulo' rIymuSnganpu' neH}.

nIqolay Q:
> Or one with somewhat more controversial grammar:
> nuH 'oH thalaron woj'e', lulo' novpu' rIymuSnganpu''e' je
> "Thalaran radiation is a weapon, aliens and especially Remans use it."

I really really *really* like this! But why do you characterize its' grammar as controversial? I can't find something weird in the grammar of this sentence.

And reading your suggestion, I got another idea too:

nuH 'oH thalaron woj'e', lulo' nov, 'ej lulo' je rIymuSngan'e'

I hadn't ever thought of the possibility of using the {-'e'} with the {je} "too", but I think that perhaps it could be another nice way of expressing "especially".

Again, thank you all for sharing your thoughts. Your messages gave me many beautiful ideas and options.

--
Dana'an
https://sacredtextsinklingon.wordpress.com/
Ζεὺς ἦν, Ζεὺς ἐστίν, Ζεὺς ἔσσεται· ὦ μεγάλε Ζεῦ