I never place or slide a frame face down on the bench - I always use a sheet of regular foamboard on top of the bench and place the frame face down on it - that way I don't have to lift the frame to rotate it - just turn the foamboard like a lazy susan - it's easy to see that the foamboard is clean, and it's cheap to replace if it gets dirty - and I have several pieces next to the bench in different sizes to suit whatever I am working on.
Since all my frames are similar (yawn) and since I get a lot of orders for a bunch of the same frame, I have a tendency to have many frames on my fitting tables at once. I have two fitting tables and depending on the size, I can have anywhere from 8-16 frames in progress on them. Since everything is similar, it's very productive to be working on them together.
I don't have the space to put foam core on top of the table surface - that's why I need the carpet. Frames don't get rotated - I don't have the need for that - but as I'm fitting more frames on the table, they get move, sometimes slid, around.
Today was typical; I did 11 Value Frames (see my site for what a Value Frame is) using three different mouldings - all the mouldings were 1 3/16" to 1 1/2" flat mouldings; two bunches were black and one bunch was a walnut finish. I cut and joined all eleven first and placed them on the fitting table, next cut acrylic for the bunch and then cut the foam core backings and placed the bendable framing points. Then bumpers were applied, stickers added, the frames turned around (picked up and turned, not rotated since I don't have room for that) and hang tabs (for opening the back) was added to the foam core backing and the saw tooth hangers were screwed in. The frames were all turned over, inspected, hangers, instructions and business cards attached and off to be packed and shipped they went.
My environment is more a production one than a one frame at a time setup. When I had a storefront, I only had room for a single table that had to be for everything, mats, glass, fitting, et all. I was constantly scrambling between frames so something like you described might have worked for me then.
Now I have 2 4x8 fitting tables, a 4x8 mat cutting/glass table, a 4x4 table next to the vnailer, a 4x8 open frame staging table, a 2.5' x 7' workbench for shipping and wood working and a 4x7 off feed table for the table saw (for acrylic). With the number of frames in progress at once, I need the entire fitting and vnailing tables to be covered by a non-scratching substanc.