I'm pretty new to fox myself but I can give some advice.
-SHL is useful for when you just need a few more % or need to force them to do an approach. Learn the variations of SHL from Melee fox/Falco discussions (actually just like go there and you'll find all the answers.
my number one tip for converting off of your foe's mistakes in the neutral is to use dash dancing to keep your options open and let you avoid attacks with a quick wave dash back or a smart spot dodge (or just run in and clank/interrupt them with teh_shine, it often works well) while you wait for them to flinch and spot dodge or whiff an attack, (fox is very scary when he DD's) then run in dash>JC Upsmash or JC grab>uthrow>Uair (or chaingrab if they are a spacie), falling Uair, SHFFL dair>shine etc. the possibilities are endless!
Just be creative, watch some vids to get ideas, play often, and don't get predictable.