That seems excessively high to me for single wall pipe.
People here make quite the claims about the difference double walled stove pipe makes. I have no reservations about this truth.
I just thought the double wall would maybe prevent adding an additional section of class A and an unsightly bracket. It would also be the easiest way to tell if adding more height would help. Would be worth a shot. Lots of online chimney suppliers if your supplier can’t get it.
A lot of old timers didn’t believe in a cap. Some still don’t. My masonry chimney has never had a cap in almost 70 years. Not saying I agree with that or not, but I see pros and cons, mostly benefits to having a cap…but I didn’t and still don’t want just any cap. So, I’m still searching and researching. Like you I’m prone to down drafts, but not from high winds…from living in a narrow valley with hills on three sides. My issue isn’t constant so I’m in no hurry and will likely add a cap when I do chimney repairs.
My pretty extensive research this far on caps led me to the conclusion that there are a lot of custom caps out there to catch customers with no real science behind many designs. For instance some sit high off the chimney exit, some seem far too low. A lot of them are super expensive, and from reading little to no consensus on which ones work best and which ones don’t. I’ve seen a lot in person and in pictures stopped up and iced up with ice cycles hanging from them at -26below. I’m just saying …
…ask around here. Ask Begreen, BHoller, and regular forum folks. What brand, style, etc. Get peoples opinions and experience, keep asking questions and try and make the best informed decision you can.
Some have conical inner designs (like a cone pointing downward) that allow any condensation that might accumulate at the top inside of the cap to drip straight back down into the chimney. Those can be hard to find and $$$. Others seem like a kindergartener designed and built them. They just aren’t all the same, nor do they all work the same. As some have said already, some caps are made for special applications like high wind, condensation at the top, to stop down drafts or swirling winds, etc. The information doesn’t seem to all be in one place either.
My point in all this, be careful what you let someone talk you into.
Just my 2 cents…