My dad is one of those funeral directors who still uses his hearse for local removals. House calls, nursing home calls; even pulls into the emergency garage at the local hospital with it. Says he has had more positive feedback resulting from the "respect" factor, so he'll keep using it. While he got his start in funeral service working for funeral homes that believed in using a hearse for removals, he has kept up the practice over the years, even as colleagues have switched to minivans.
If you talk to my dad about this, he will explain that countless times over the years, right up to now, many families have accompanied him out to the vehicle. Often, someone will comment how glad they are that he brought the hearse. The nursing homes in my hometown have now adopted a new program of "ceremoniously" escorting a deceased resident from the facility. This involves prayer, the placement of a special quilt over the cot, and participation by staff and family. They actually prefer that the funeral home bring a hearse.
So, having grown up around my dad's funeral home where standard protocol was to use the hearse on removals, the only "extra" thing we really needed was something to protect the rear floor when the cot was rolled in. We used a color-coordinated piece of carpet remnant. Our rule was - and still is today - NEVER put a cot into the back of a hearse without something to protect the floor, hardware, and rear bumper.