Good Solar Path LEDs for cloudy weather
Possibly, but you'll need to refine your purchasing skills.  All these lights have an engineering balance of solar panel size, battery size, lamp consumption and cheapness. The problem is, as you have identified, you are in an area which has a lot of cloudy days, and as such, much less solarization than average America. 

You have "gone straight for cheap, modulated somewhat by reading reviews". Generally the products are designed for reasonable performance in the first day of service in an average day (i.e. equinox) in more sunbelt-ish America.  Most of the cheapies I have seen don't make it through the night, meaning they fall to zero every night, and rely on a sunny day's worth of charging to even make it to midnight.  That just isn't going to happen in Seattle, where solarization is lower than appears to the eye.  (Eyes aren't lux meters, they are designed to auto-adjust and effectively conceal absolute light levels from the user.) 

As such, you need a specialty product, and so I'd be looking at the "specialist geek type" small manufacturers, who are designing high-performance lights for your service demand. They will have a solar panel and battery that is outsize large compared to the lamp.  The prices will not be what you're used to.  If that's a problem, then you can look at hardwiring either mains or low-voltage lights by burying cable or conduit.