Thinking about it, I think I spoke (er, wrote) too quickly when I said I couldn't think of quick-build options.
I still think one of the best ways to make drivers more cautious when turning left onto Grove from Highland would be to reverse the direction of one lane of traffic to reduce drivers exclusively looking to the right because that is where other drivers approach from. And similarly, we already agree raising the crosswalk to function like a speed bump would get drivers turning and going straight to proceed with more caution there. But as I said, the city will likely insist that wait until the more comprehensive Highland reconstruction.
What I hadn't considered was how much open space there is on the street there. Adding paint & flex-post curb extensions to narrow the perceived road width on Grove and Highland down to the standard lane size near that intersection is something the city could do (relatively) cheaply, and would still encourage drivers to move with a bit more caution.

(Obligatory disclaimer this is just a rough sketch, and I am not professionally this type of engineer, so as much as I have learned a ton from people who are, there might be issues with this design that aren't occurring to me right now.)
Frank also brought up the point many drivers going straight on Highland are more focused on the traffic light than the crosswalk. I wonder whether the city would consider installing filters on the traffic lights so they aren't visible until you are at least through the Grove St. crosswalk, and drivers can keep their attention on pedestrians, bike lane users, and parallel parkers that much longer. That wouldn't address the Grove St. left turn issue, but I could see it helping with speeding on that bit of Highland. Unfortunately, I don't know whether that stretch meets the conditions for those filters (obviously drivers need to be able to see a red light far enough ahead to stop safely).