You are probably better off returning a smaller dataset that will return quicker in a fetchall_arrayref, ie. only the primary key, and then fetch slices through that list.

select ID from hit_table
where time between ? and ? 
order by visit_id, time
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Then loop to fetch 20 rows each time using something like :-

select * from hit_table
where ID in ( ?,?,?,?,?, ?,?,?,?,?, ?,?,?,?,?, ?,?,?,?,?) 
order by visit_id, time
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Hope it helps
UnderMine