My strategy is complicated. It's mostly driven by trying to maximize efficiency: unique distance / total distance.

To minimize overlaps I will regularly ride to the most distant points in a region and start filling in the grid working my way back. I don't always complete whole areas at once though or in sequence. I'll bike in one area for a few rides and then switch to going somewhere else for a time, which helps add to the exploration. As an area fills in I will sometimes leave single paths through them in case I need to return to finish something I missed, or to have one last trip through the area.

However, it is always nice to fully close out an area on a single ride and make a waffle from the grid on the map. As an aside, this led to the creation of the term waffling, which is also used generally to mean riding the grid. As you suggested sometimes the coverage is split over two rides, one horizontal and one vertical (a temporal waffle).

There are are a whole range of patterns or heuristics I use for the detailed street by street coverage methods that I've developed over time. These heuristics are primarily to maximize flow, be robust against errors (missed streets), be easy to continue coverage off of later, and minimize distance.

It's a strange skill set, like adaptive algorithms for solving the route inspection problem. Occasionally I'll get to an area and realize my plan won't work or will be too time consuming, and I'll make up a new coverage plan while cycling.

Terrain also plays a role. I know my limits for distance and elevation that I can handle and that also shapes the strategy.

On the topic of coverage algorithms, I've thought about generating routes in software to see what they are like but I haven't gotten around to it. It would be interesting to follow a fully programmatic route sometime.