Ideally I'd like a solution to stay bone dry.

This would be ideal, of course. Here in Oregon I've tried a lot of raingear solutions over the years, but that danged 'ideal' one hasn't ever materialized. However, I do think you can improve quite a bit on the experience you described.

The rain getting in at your neckline sounds like a seam leak to me. You could look at putting on a sealant. The rain getting in at your open sides is just one of the weak points of a poncho.

The Campmor rain cagoule TomD linked to is a good piece of raingear and it will cover you down to the vicinity of your knees, like a long coat. And it is a fairly low price for decent raingear, unlike the super-fancy stuff out there that can run you over $200 at its worst.

The advice to ditch the jeans is good advice. In heavy rain, the water runs down the outside of your rain gear and anything exposed beneath its bottom edge gets a river directed onto it. Cotton jeans soak up water like a a sponge and then takes two lifetimes get dry again. Anything synthetic (nylon or polyester) in the way of pants will be an improvement. At least it soaks up less water and dries faster.

If you want your pant legs to stay "bone dry" (or something like that), then you'll need to intercept that river that is dripping off the bottom of your raingear. You can go with rain pants, or, if you can find them, you can look at rain chaps that cover just your legs.

The problem with all rain gear is that the more completely it covers you and excludes rainwater, the more completely it traps your body heat and sweat. If you are exerting very heavily (carrying a pack, climbing a hill) this means quite a lot of sweat gets trapped. Then the trick is to ventilate in such a way that some of that heat/moisture escapes, but little or no rain water gets into the vent holes.

There are many solutions to this venting problem, some very expensive. Pit zips. Back flaps. Gore-Tex. eVent. NONE of them are perfect or even especially good. All of them help somewhat.

You'll need to figure out what most PNWers know. If you're really working hard in heavy rain, bone dry is not an option, but you can get the moisture down to a middling amount of steamy dampness, rather than purely soaked sopping wetness.