"The use of the EDNS(0) padding only provides a benefit when DNS
packets are not transported in cleartext. Further, it is possible
that EDNS(0) padding may make DNS amplification attacks easier.
Therefore, implementations MUST NOT use this option if the DNS
transport is not encrypted."
Apparently it does have a padding proposal, but it wasn't thought through very well. They only had the use case of confidentiality in mind, and decided to deal with amplification by forbidding cleartext use, no matter what the response:request size ratio is.
So, yes, I think padding it could work. (EDNS does have a padding type)