Yup AHL stock shoes are so so too. Remember i used third party shoes in Deluxe rear brake for better braking.
Using stock rim/tyre at rear since long time now.
Had agility issues with 100/90 tyre, and offroading/wet grip issues with 90/90. So came back to stock dual purpose 3.00 tyre and changed the rim back to stock too.
Front rim is replaced with Deluxe 1.6 rim though. Except that total stock.
This bike actually needs some decent brake shoes more than wide tyres. Try decent shoes first, and if still not satisfied then think of bigger tyre/rim setup.