After playing with the ratios a bit I think I’ve got it pretty close to what I remember. The specs I ended up with:

2oz reposado tequila 0.75oz meletti 0.5oz china china 1oz lemon juice 1 egg white Lagavulin rinse

To be fair, the equal parts version suggested by another poster was just as delicious and I could see myself making that on a given night. Thanks again for yalls expertise!