Getting Number Of Reads In Intervals With Bedtools

What is the correct way to get the total number of reads strictly contained in each interval in a GFF from a BAM file while enforcing strandedness? What I am looking for is very close to this intersectBed feature:

-c    For each entry in A, report the number of overlaps with B.
    - Reports 0 for A entries that have no overlap with B.
    - Overlaps restricted by -f and -r.

Except that I'd like the number of overlaps in A for each entry in B (i.e. the other way around). If I do:

intersectBed -abam mybam.bam -b mygff.gff -s -f 1 -wb

Then my understanding is that this will report the entry in B for each overlap with A. But I'd like each entry in B to be outputted exactly once, with the number of reads from A that are contained strictly within it. I'm not sure how to enforce strict containment here.

Is coverageBed the solution to this? Or multicov? I'm not sure how to enforce strict containment using coverageBed - it's not clear to me if that's the default from the docs. Thanks.