In regards attention and movement; I heard from a trainer that for kids who have trouble staying still, exercise prior to the lessons -as you well stated - will help tremendously, I also heard that some moms use in door re-bounders or a mini kid friendly trampoline and while they jump they are read or given the BITS - it is proven that kids will absorb better the information while in movement so this may even work on your favor if you find what worked for your child, every child is different.
Another thing that has worked for me is the use of little puppets to read instead of me reading... I notice that as long as I make it fun - goofy - ridiculous , Leena will remain engaged - the silliest the better! One time I remember I didn’t have anything handy and we were in the middle of a lesson and I really didn’t want her to lose interest... in a flash the only thing I could think about was to add two red dots (eyes) and a smile to my rubber finger (used to count money or to help you flash the cards quicly) and I loudly said hey Mrs Pluto is here to help today...!! She looked at it... and crack laughing... guess what.... now Mrs Pluto is a member of "our school" she teaches her the presidents, states and planets, once she is finished another "creature” - meaning another rubber finger will join us ( I must make it cutter maybe a tiny wig or a mustache drawn with a marker) and teach her something else LOL )
Hope this helps
Gloria