Mosses tend to Bloom last 2 weeks of May here in NYC but everything tends to be exploding about the same time.

Mosses bloom approx the same time as gallicas.
Olga

As Olga has suggested, the mosses don't significantly deviate from the timing of the rest of their relatives of the Gallicanae. You will occasionally find an individual that starts a week later than most others, and ends a bit later, but the timing differences are very subtle indeed.

Repeat flowering Mosses flower later . . .

In my garden the once-blooming European old roses all seem to bloom more or less at the same time: from about mid-May through mid-June. Among roses, some of the ramblers may come later, but I'm not sure. After the big first flowering ends around mid-June it's hot and dry, and not much happens in the rose world until temperatures begin to drop in late summer and the reblooming roses get going.
I wouldn't look to roses for blooms or other garden ornament in high summer. Lavender flowers in the summer, if I remember correctly, also trumpet vine; in Washington state some of the large-flowered clematis began flowering when the roses were finishing up. Buddleia is good for high summer. The point is to think of succession of bloom. And summer is so bright and hot and dry here that I don't even want to go out in the garden. Instead I stay under the pergola or find another shady spot and admire my begonias and sansevierias. Some of this will depend on your climate, of course.
Good luck in your search.
Melissa

Thank y'all so much!

That does sound like it would overlap with so many roses. Good to know!

I don't grow any gallicas yet, either. I will; they are too gorgeous not to try.

Melissa, thank you!, that's what I'm trying to accomplish this year -- the earlier and midtimes that I've missed :) Buddleia is wonderful. That would be excellent in this intensely-colored garden I'm thinking of, as a matter of fact. I'll probably put Crimson Globe by some bourbons and HPs I have that go with his colors.

I never can grow lavender well here with the acidity and humidity, but I found a salvia and one nepeta that fool the neighbors :D

I do go out in high summer, but I'm specifically planning some shady oasises close to where the chores are :D I should have done those areas first!