To me the retractable awning is what you need but of course will not stop that late afternoon sun . Maybe the best would be a wall mounted rectangular tiltable umbrella I can’t really see how a roof structure will have any effect on the late afternoon sun I do agree I love the sun heating my house in the winter

I have never seen that kind of umbrella, neat!

Those boulders heat up and throw a lot of it against the house too! You might explore planting rock garden plants that fill crevices and cover some of its surface. Do you have High tech UV film on the windows/slider? My triple bedroom window faces west and in summer a black sunscreen is hung over them. My neighbor followed suit and hung them all along their front porch. Not pretty but they do the job. Both our houses face the street, but we're out in the country so who cares! Maybe just film on the door so you can enter/exit and a hanging sunscreen over the windows. I winter you store away the hanging sunscreen.

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The doors and sunroom glass are low e and the overhead panels are slightly tinted. The extra heat in the house is an issue, but not the main one. Its more that we want to be able to sit out there without being blinded and baked alive.
@patricia - DH was thinking with a structure out there, he could put louvers or a roll down blind on the side to block the afternoon sun.

You can use the sunscreen on top of the pergola in summer and remove it for winter.

Sounds like a pergola with a sliding/remove-able sunshade might fit your needs by providing shade in the hot months but still allowing sun in the winter. There are lots of options from DIY outdoor fabric to fancy pivoting/sliding/motorized options. I was looking at the following option for my own house, but I'm guessing it is not cheap.

https://struxure.com/products/pergola-x/

Lots of other ideas if you search for retractable pergola canopy on Houzz or the web.

So many lovely options! I like the idea of a pergola, I'd just need to figure out where we can place supports where they won't be crowding the walkway.

we've done a few of these covered patios on our home and our rental. (and we built one for the neighbors!) you can use slat wood (we did 1x1's) but you can choose a wider size and place them as close as you like. it really help avert the sun. on ours at home we covered it w/a landscaping sun shade material. really works well.

here's the one at that rental. you can see the posts aren't a big deal with foot traffic.

the main header beam gets attached to the side of the house, and you build out from that.

Maybe you could have a contractor drill into the stone for the supports so as not to impact your walkway.

We had a pergola installed over our deck which also faces south. The pergola alone does not shield you from the blazing sun. As a resul, we have ordered a retractable shade for the roof and a pull down solar shade for the west facing side. They can’t come soon enough!

@nhbaskets - what type of shade did you order?
I'm thinking possibly just a modern looking box frame and the retractable and side shades as well. The Roman style shade seem to be the most cost effective but they don't 100% suit the look we're going for.

We’re getting retractable shade from a semi-local company but it’s from ShadeFX in Canada. Pull down shade is a Bali Solar shade from Lowe’s.

ShadeFX: http://www.shadefxcanopies.com/for-home/

Bali at Lowe’s: https://blinds.lowes.com/product/detail.action?sku=Bali-Exterior-Solar-Shades&groupName=Bali&xdata-width=24&xdata-height=36

Another company we looked at was Infinity Canopy: https://www.infinitycanopy.com

Consider shade sails for a shorter term, flexible option. They might help you prioritize what you want longer term. We have a couple, with multiple attachment points so we can configure them in different ways depending on the time of day and season. If the grandkids will be here using the pool at high noon, that looks one way, if we plan to have a crowd on the patio in the late afternoon, that's another.

Thats a great idea!

Other options depending on the type of weather coverage needed include retractable pergolas for:

Sun protection only OR

Both sun/rain protection OR

Sun/rain/hail and snow protection

For sun protection only the Perugia model slide on wire canopy here is perfect. For both sun/rain protection consider one of the many retractable pergola options here and for snow protection, the bioclimatic Bioclimatique rotating louver roof model here or bioclimatic Bioclimatique model retractable louver roof model here is best. The best option since this model can be both tilted and retracted may be the Torino model here.

To cover the sunroom you can use the Verona retractable pergola model here. It is designed specifically to be used to cover sunrooms, winter gardens, pergolas, and greenhouses. Two Verona model pics are below

Your yard is very pretty. It's hard to tell in pictures which corner is the SW side or if you have room with the rockery but would it be possible to plant a tree to offer some shade? Something decidous would allow for winter sun.