This company do expect their drivers to climb in and out of their double deck trailers when at customers sites, most of whom don’t have bays.
I spent the first two months of this year doing bulk C&D for them with DD trailers. My technique for climbing up from bottom to top deck was to use the middle ring on the side of the top deck frame as a hand hold, but it’s a stretch to reach and still a big step up for me at 6’1” tall.
The strap inside the trailer is only helpful when climbing onto the bottom deck because your body is outside the trailer, once inside the trailer the strap is at the side of your body and using it when attempting to get onto the top deck just rotates your body increasing the chance of a fall.The strap can’t be repositioned further into the trailer because it would be behind the side of the top deck (where the ring is).
Fortunately I was able to get a change from C&D back to trunking by telling my agency it was just too much handball, but still occasionally have to climb in the trailer as I do various shifts across three different depots now (my choice).
However that option probably isn’t open to a directly employed driver.