I’m the developer of Reduce.jl but am only on my phone internet for now and don’t have much time to look into this problem right now. If you do try something, let us know and I might be able to help, but I don’t have time to really work on problems at the moment.
The package does have features for declaring a symbolic variable as linear operators and matrix / vectors.
You can also reach out to the sourceforge community for the upstream REDUCE, they are also helpful there.