Search post overlapping dates - meta_query with meta_key

Question

I'm having a search form for rentals that search locations available according to a date range.

For now, I store all reserved dates for each posts as post_meta. For exemple ;

post_id: 231 post_meta : location_reservation_start : 2022-09-02

post_id: 231 post_meta : location_reservation_end : 2022-09-08

post_id: 231 post_meta : location_reservation_start : 2022-10-02

post_id: 231 post_meta : location_reservation_end : 2022-09-02

(multiple meta_key for the same post)

There is the query :

        $start_date = $dates[0] ;
        $end_date = $dates[1] ;     
        $date_query[] = array(
            'key'     => 'location_reservation_start',
            'value' =>  array($start_date , $end_date ) ,
            'compare' => 'NOT BETWEEN',
            'type'    => 'DATE'
        ) ;
        $date_query[] = array(
            'key'     => 'location_reservation_end',
            'value' =>  array($start_date , $end_date ) ,
            'compare' => 'NOT BETWEEN',
            'type'    => 'DATE'
        ) ;
        array_push($meta_query, $date_query );

This code work if there's only one post_meta for post. As long as the post have multiple same meta_key, the NOT BETWEEN doesn't seem to work.

There is a way to make it work like that or should I store the reservation dates in a post_meta serialized as an array?

Thanks