July still holds the chance for snow pockets, at least on the Sunrise side. This looks like an early summer picture in Paradise, likely July too, due to all the avalanche lilies blooming. You're likely going to see mostly those, and maybe some pasqueflowers starting their cycle if you go in July.

Holding out for after Labor Day could give you more color, but you also have to consider the crazy wildfire smoke we've been getting the past couple years because it hits the mountain too. That time is also the busiest for the park because people are wrapping up their summer travels, and it means that some of the flowers will stomped by off-trail visitors. The weather will be unpredictable as well, higher chances of rain and sleet.

I hope this info helps! It's just based on my one summer as a ranger there :) Congrats on your marriage!