Your process of mashing seems good. Efficiency isn't as important as consistency and it seems your process is consistent.
You are not milling your own grain and you don't know the gap on the lHBS mill so I would start there. Even if you mill twice if the gap is too big you won't get a good crush. Mine is set to .035 which is 1mm so I would check that first or get your own.
Have you checked you ph? Ideally around 5-5.2 is good for conversion purposes and how is your water? Water chemistry can play in as well.
Also as mentioned how much wort are you leaving behind, if you reach your pre boil volume before the tun is drained you are leaving behind a lot of sugary goodness!
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