How to build a removable bench for a sit-in window?
Too long for a comment. A photo of the area would help, in my last house I had a large window seat that I cut tongue and groove boards to cover the seat and make a removable deck that fit the space we put our downstairs tree on. 

This is reverse to what you want to do but may work for your needs. I cut each of the boards to fit tight in the space. Your miter saw saw is all that will be needed for this. After making sure everything fit well, I attached a small piece of wood molding on each end to hold them in place. I then sanded the tops and stained the boards. When we wanted to put the deck in the smallest board first pushing them together it held in place nicely. We had 4" foam covered cushions made to fit the seat I did add some Velcro strips to the bottom of the cushions to hold them in place. We never had any problems with the windows being leaned on (the sill was less than 12" above the seat). 

I think this is a good possibility for a DIY project the only question is the support from the shelving units. Or adding a small ledger frame on each side to support the seat and a center support because of the span.