The first place I would start is with a value stream analysis (or going old school PMP, a critical path analysis).
Start at the beginning of your process and start mapping out each high level task, Determine what the inputs (dependencies) and outputs are for each step. Record the cycle time for each step (how long does it take to perform). Once you've got this mapped out it gets a lot easier to see where your process is taking a lot of time.
A visual view (white board, post its on a wall, etc) works the best as it engages your brain differently.
Three thoughts, based on what you've mentioned:
Hire a consultant to help you with your process reengineering. It is so very easy to get lost in the trees and not see the forest when you work inside a company. Bringing in someone even for a day or two can often be exactly what you need to to get a viewpoint that will break you through to your next level. Think of it in the Bill Gates Dollar metaphor. How much time will you spend working on it that you are not working on building value for your client backlog? Is it worth your time to pick up the process improvement dollar on the street?
Kanban may work better than Scrum for your work. Trying to plan sprints around the work is going to be a lot of overhead with remote teams. Also, most of the work you're doing is probably "repetitive" in that each client wants much the same thing. Kanban works well for this.
Limit Work in Process. How many things are being done at a time? Where possible break down the work into smaller chunks and swarm the work. Instead of ten sites at one time, with one developer each, swarm on two sites with five each. Requires more coordination, yes. Even with a remote team it can be done. Published a 300+ page, 20 author, 10 additional staff book with an all remote team using email and chat only this way.