Beautiful!
Being in the northeast like you, I tend to be a sucker for masses of billowing color after our long, long winters. I could see a few small boxwoods for evergreen structure--easy to prune and keep within bounds--and if you DID want color, combine them with masses of super easy Wave petunias, and other perennials mixed in as an accent to the phlox and soften the lines of the steps.
You could do an all white palette, which would be cooling and soothing but still work well with your desire for largely green.
I personally love riots of color though:

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Okay--I'm not seeing the juniper as a problem, so maybe I need to know more about your goals and what you want this area to look like. The juniper does not look overgrown to me, and is perfect for a slope in hot sun. Why do you want to replace a mature green groundcover with an immature one?

The flowery photo above is a very high maintenance look that will be bare in winter--okay if the area does not require erosion or weed control and you don't look at it.

Staying away from specific plant recommendations at this time, my question is to identify what you're after, and maybe work on the existing bare areas that are flatter before you rip out the junipers. Think that if you want more color, even like that in the photo above, you could start by introducing annuals and perennials in the bare spots--IOW, develop some planting pockets for color amidst some established evergreen groundcover. These could be directly in the ground or in containers. See how that works for a season.

Off topic, what kind of kids do you have, that can't get over that fence?

NYCynthias and Frankie -- thanks very much for your thoughts.

NYCynthias -- yikes, your yard is stunning. You certainly set our minds turning in terms of colors. I too was considering a line of small boxwood down the stairs.

Frankie -- too be honest, my wife has been on me for years to remove the Juniper. She just doesn't like it. It did become overgrown for the space a couple of years ago and I hacked it back. The picture doesn't show it, but the areas right along the stairs are thick, viny, and unattractive branches, and it's started to turn brown in areas.

With regard to the flat areas, my wife has usually loaded them with Impatiens.

I guess the look we're seeking is traditional classic though by no means stuffy, dull, or colorless.

We have young children and the fence -- 4+ ft. with 1x1 in. wire fencing -- keeps them from from wandering in when we're not looking. It would certainly look nicer if we were to expand the fenced area and run the fence right to the ends of the house, but we'd rather they and the dog have the run of the backyard.

That silvery-gray fence is just crying out to be draped in pale blue clematis! The wire backing makes a perfect climbing frame for the clematis....

Three pieces of Dwarf Fountain Grass (Pennisetum 'Hameln') in a triangle up by the top step would be attractive. Full sun, an excellent summer flowering ground cover is Plumbago (Ceratostigma plumbaginoides). It's vivid blue flowers would go with lots of other colors, orange or yellow marigolds, for instance.