I remember heads from a long time ago that had gearing to allow them to put out two different rates of water but I don't know if they every made it to production or if they did, I've never seen or heard of them since, so they were not widely used.
Most systems now are built with two sets of sprinklers around the green, with one set that can be set to water just the green and one to water the surrounds (or bunkers, approaches etc). Personally I have the greens set to 360 and the surrounds are partial as I like the deep soak of everything when we water greens. Most now have individual control and can be run from a cell phone and the desktop software allows for infinite tweaking of run times etc.
As for the sand issue, it is your bunker sand. I don't think there is a perfect bunker sand, solely because of peoples taste, with some liking firmer ones and some liking softer ones, it can only be one or the other. The bunker sand I used for years was great but it firmed up a lot when wet and there were complaints that they were too firm, although when we switched to machine raking them, that went away as the surface inch was agitated, but if they were not raked, the complaints would start again. The moisture levels played a part in it too as when they dried down, the sand would get a bit fluffier. When the bunkers were redone this year, we tested a number of sands and the the softer ones were consistently picked. Spec wise they are similar to the other one but it never firms up, no matter how wet it is, but the negative is the ball sits a little lower in it. Now the complaints have switched, those that didn't like the old sand, love these and the ones that liked the firmer sand don't......
Bunker liners can help as they create a perched water table so the moisture in the sand can be manipulated somewhat by the depth of the sand. The issues with that is if they are kept too wet, then algae can appear on the sand surface, and there is a fine line between wet and dry (ie maintaining the sand depth is important). On the flip side, while they do a great job with preventing washouts on the faces, I think that the the sloped perched water table on the face causes them to dry down inconsistently, which can cause softer sand on the faces. I have to play with that more to see if the moisture on them can be manipulated by having much less sand on them, while still keeping enough there to prevent a club hitting the liner.
There are a lot of variables at play so it is hard to maintain bunkers to keep everyone happy. It would be nice to go back to the old days where they were just a hole where the sheep slept!