Sounds like you have a killer coticule there. Congrats on the thuri. I always make a thin slurry on my thuris that i do a quick dilution on. I then finish on thin/trace slurry.
but you should try both to see what you prefer. It works both ways. If I skip the linen on my strop then I'll double the number of laps on my leather strop.
Funny thing on my lighter softer thuri I felt an improvement on skipping the linen but my darker harder one benefits from the linen leather strop.
Here are my thuris I had a third one but gave it away.