Adding a random amount of random bytes will not defeat the attack, it would only slightly increase the amount of time required by making the side channel noisier.
Adding a fixed amount of random bytes will have no benefit at all.
Not following your assertion. Suppose the reported size was always a random epsilon larger than the actual size. Choose epsilon so that its small enough to benefit from compression and large enough to obscure the BREACH. Why doesn't that work?
Adding a fixed amount of random bytes will have no benefit at all.