Something else to consider is getting a tarp and a couple of extendable poles. I got these when they were on sale for $25 (Amazon Link). Setup is fairly easy and just have to use guy ropes on each corner to hold it down, but takes up significantly less space than the 10x10 folding one. I usually attach one side to my roof rack, but I have 4 poles so I can move it around and make it stand alone. All-in was just under $100 so about the same cost as a bigger canopy.
I use one of these https://luxe-hiking-gear.com/products/batwing-group-lightweight-tarp
Combined with a set of Green Elephant Telescoping Tarp Poles | Adjustable Tent Poles for Tarp Set of 2 | Portable & Lightweight Aluminum Tent Poles Replacement https://www.amazon.com/dp/B072K1B91Q/ref=cm_sw_r_cp_api_glt_fabc_GKYGJX46B45H9MNBNC19?_encoding=UTF8&psc=1
Makes an excellent rainfly to cover both the tent and give you a nice area underneath to hang out because it’s so large, and plenty of space for shade and airflow.
I would not use that stand to hang a tarp, no. Way too short.
I suggest you get two telescoping tarp poles like these and hang up your tarp over your hammock stand.
I ended up getting something similar ... https://www.amazon.com/gp/product/B072K1B91Q
We got a light blocking tarp that we put above our tent to keep it cooler and darker in the morning. I hold it up with the poles I linked to below. It requires a little work to setup and tear down. I had to basically use guy wire on all four sides to keep it from falling over.
I got four of these: https://www.amazon.com/gp/product/B072K1B91Q