I've only seen one diameter, approx. 2.5 mm I think. Strength is usually "50lbs"
But the sleeving on factory made kite lines seems slimmer, so if you have a choice, probably the thinner one would be the one to try first. The everyday cord I see is slightly bulkier but it works.
Next time I customize lines though I hope they will be all 4 800# spectra with no need for any sleeving anywhere.
It has to be the 12 strand braid which expands for splicing.
The 600# kite lines lines in my experience are 10 strand and don't make a tunnel when you try to expand them.
I am rather tired of how the sleeving tends to hang up and encourage twists etc.
bwd as far as I know the 600's are also 12 strand and I have no trouble splicing them, all manufacturers, no problem. I have not seen a 10 strand 600 pound line yet.
My fid is made from a sharpened bicycle spoke, I tape the line to the end, it goes thru really nice even when the lines are dirty and full of sand and mud.
You might want to try using a different fid but I am with you on the 800 lines the 600's snap too easy even brand new.
I agree with your advice on finding sleeves, just go to the store, look around for some line u like take out the center, replace with kite line.