Your engineered trusses are almost certainly designed for insulation and drywall loads. I've never encountered a situation where they weren't, and I've been involved in residential construction almost since that garage was built. I wouldn't hesitate to finish the ceiling.
Use no-sag 1/2" drywall to reduce weight if you like. Just use some sense when loading the attic for storage. Spread the load, keep heavier items near the wall, and don't go nuts. A few hundred lbs. is about what you can reasonably do. If you ever get a zillion feet of snow at a time consider removing some near the middle.
Secondly, a proper solution to a situation where you did need to bolster the roof system doesn't involve a bunch more joists. It would likely be a single large beam down the center, directly under the vertical truss members. You'd then still attach drywall to the existing ceiling framing and wrap the beam. No need to lower your entire garage ceiling.
That said, beams under monolithic engineered trusses are very unorthodox. This type of truss has an expected seasonal deflection (called "truss lift")--as they heat and cool and absorb moisture and dry out they rise and fall at the ceiling line. A beam would be likely to have a gap over it half the time.