Thanks for the update. I'd say that's looking pretty good. Filtering through a cotton plug should clear up much of that cloudy lime residue - but see also below.

Your concerns about lime carry-over making its way into smoking mixtures can be allayed somewhat in knowing those particles will most probably be calcium carbonate already, or will otherwise get converted fairly rapidly on storage. A deliberate treatment with carbon dioxide may be worth considering, if there seemed to be excessive lime residue.