In addition to the other good suggestions:
Actually some parts of Froggatt can be quite accessible if you take the approach from the roadside parking bay along the good path which leads along the top of the crag from the L hand side as far as where the quarry track leads down to the R hand end of the crag. Flat, well surfaced and lacking stiles but maybe approaching your distance limitations. (presuming the undesirable approach you mentioned was up through the woods from near Chequers pub)
Baslow edge is pretty short and accessible as far as the veiwpoint. A slight incline from the road.
The right hand end of Curbar has a fairly short approach on good paths but is a little uphill till you get to the crag. The path down to the crag base is a little narrow and the hillside quite steep in places. Not sure if there is an easier path down further along near the avalanche wall area.
Shining Cliff is a short flat approach if you park up in the woods near the hostal
Burbage S boulders allow blue badge holders to park through the gate beyond the small (usually full) carpark before the road crosses the river. This is the start of Dukes drive, quite a lot of the boulders are close to this.
Chatsworth is a short approach to the lower parts of the crag on the side of the path. There are some steps however to get down and over the stream and maybe a stile or 2 (can't remember).
Burbage S crag from Fox House is a fairly short flat approach. It does have stiles and uneven surface however.
Obviously the accessibility of all of these are highly relative to each individual. The nature of the descent paths and crag bases are another factor which might affect your choices. Doing a recce could be a good plan if you have any doubts.
Post edited at 15:11