4x4 Reflector boards are very useful. You can hit an actor with a rim from a pretty good distance. Also use them a lot on establishing shots of buildings that have an entrance under an awning. Hit some light in at the shadows so it doesn't look like a black hole. Sometimes it looks really sourcey to the eye but usually reads fine in camera. Reflector boards usually have a hard side and a soft side which you can choose based on how much intensity you need, and you can definitely also shoot them through 4x4 diffusion frames, just make sure your angles are right so that the diffusion isn't cutting the incident light on the reflector. Usually you want a technician to shake the reflector boards up every couple takes to make sure they're aimed properly as the sun moves.
I work with one gaffer who likes the 12x12 checkerboard silver/gold lamé for fill bounce for wide shots under harsh midday sun where you can't use an overhead. You get a lot of punch out of it, and I think it looks a lot more natural than a straight silver or straight gold lamé. Also you can flip the ears around and use the white side on the back, which gives more bounce than a lot of the dirty ultra bounces you get from some rental houses. This is for a TV romance series, so there is more of a textbook warm stylized look rather than natural realism, so may not fit your bill. We also created custom 4x4 beadboards with silver/gold checkerboard over the normal silver shiny side for tighter shots or tracking shots that require you to follow an actor with bounce fill.
This same gaffer also uses a 1/3 silk for overheads. He brings this rag from Germany. I haven't seen 1/3 at a rental house in the US but it could be around somewhere.
For singles, you can often get by with a 4x4 frame of diffusion overhead, either handheld by a technician or in a combi stand, depending on how high the sun is. Usually complemented with a 4x4 beadboard for fill. This is often faster much faster than moving bigger frames around, especially if you are understaffed.
If you find yourself going back and forth between bounce and overhead and you only have one frame, skin the bounce right over the diffusion rather than pulling it off every time. Saves a bit of time when you have to switch back.
There are some situations where you just have to bust out the 6Ks.