Can I add more insulation to my attic?
Based on your picture and your description, you have what is known as a cathedral ceiling. The "1-2 feet of space" you mention leads me to believe that it's built with parallel chord trusses rather than solid rafters. Can you post a picture? Regardless, like most cathedral ceilings, yours seems to be insulated insufficiently and built incorrectly (ridge vents but no soffits vents? WTF?).

Right now your cathedral ceiling is semi-ventilated. If there is a way to add soffit vents, they should be added so that the ridge vent can actually do its job. This will increase the durability of the assembly substantially if you live in a non-desert climate. If you take this approach and build a fully-vented cathedral ceiling, you cannot fill up the extra space that you see with more insulation; the ventilation gap is critically important. How high the gap must be depends on the steepness of the roof. A very steep roof might be able to get away with a gap of only a few inches under the roof sheathing. It sounds like your roof has a shallower pitch, so 1-2 feet may be necessary.

The only safe and practical way to increase the insulation of your ceiling is to transform it into an un-ventilated ceiling. Step one is to remove the ridge vent. Step two is to either apply spray foam (open or closed cell; minimum 3" for closed cell or 6" for open cell) under the roof sheathing, or else remove the roofing material and then apply rigid foam insulation boards over the sheathing, usually 4"+ of polyiso. Step three is to fill the entire cavity under the foam or sheathing with as much as you want of whatever you want. Go wild stuffing as much insulation in there as you want. Step four is to make your ceiling as airtight as possible. Remove all can lights or replace them with LED models that have an airtight fixture, and caulk everything. You don't want inside air getting into your now-unvented roof.

The spray foam approach is likely to be more expensive, especially considering the access problems you mentioned, but does not require a re-roof; the rigid foam approach is better for the environment, will give you an ultimately higher level of insulation, and may be cheaper, but doesn't make sense if your roofing material is in perfect shape.