I love the grandprix tech lite and one and the sport cut italian version (though a bit pricier). I will try and find the name of it for you but they are amazingly breathable and comfy while looking very hunter-ring appropriate
I highly recommend trying Equiline and Animo show jackets. However, they don't have the pro-air or tech jackets you are looking for but, they are extremely lightweight and very comfortable to wear on hot summer days. If you don't have the budget or don't want an expensive show coat, I would recommend trying Grand Prix. They have all different types of jackets like the pro-air and tech jackets you are looking for.
Hope this helps!