Line by line.

I gridded the project roughly with black floss. In counted cross stitch, I minimize the counting!
However, I kept piercing through the floss. It didn't bother me to have to move the floss out of the way, but piercing through out would make it a bear to remove.
Off we went to the local sporting and outdoor goods store. I picked out some fishing line- it was the most fluorescent pink-orange and flexible like normal thread. Some kind of "bonded braid" used in ice fishing. Splurged a little because I liked the texture and color.
Oh, me.
Of course it was a terrible choice. It STAINED.
Seriously! A plastic fishing line! I had pulled out my first line a few times when I noticed bright neon pink-orange pin pricks on my white Aida. WHAAAAAT??
After a small and rather understandable freak out, I pulled out an unused Aida-banded hand towel, ran the offending thread through it a few times until it left marks, then left it to soak. I think it came out... But the hand towel is pale yellow, and ended up being soaked multiple times, then dunked in diluted bleach, then washed in the machine twice... because it had some dark mystery stains which, hmph, have NOT come out all the way.
I've decided to live with the faint remaining stains-after all, it's a towel, it's no good to me if it never gets used.
I couldn't live with the neon pinpricks in my white Aida heirloom, though, so off to another store for bright red stiff plastic monofilament. It works. No stain, easy to stitch around, very cheap ($4 for 1000 yards vs $8.50 for 50 yards of staining), but, as predicted, it's annoying to work with.
This isn't the project for "traditional Celtic with pops of neon", but I've still got the bonded line- I haven't written off that idea.