We have removed the old carpet from the floor (where the cardboard is). I would like to cover the gap between the floors with a transition strip, but the issue is that the gap is hollow i.e. there isn't anything under it to install and fix a transition strip on. The gap is around 10 mm in width, but it also narrows in some part (see the image). Is there any way to cover this gap (other than a sealant or a gap filler), so that I can screw a transition trip on to? or a better way of covering it? Thanks.