Add coverage to the non-printing area. Either a tint or a few solid shapes in roughly the same coverage as the live area. if the work is centered on your 40" sheet, have your pre-press tech add coverage to the left and right of the art. You can keep your density lighter than usual on these areas while keeping ink and water supplied across the sheet.
You can also add take off - In-line with the artwork - if you find your densities climbing to no avail. This would be just blocks of color before and after the artwork (same as whatever the live work is). Just something to ensure ink is taken off your rollers (and fresh ink applied) and not piling up from so little coverage.
We used to run a single, small blue logo. it was maybe 3% coverage at best. The blue would get dark, pressman drops the flow/keys, water takes over and washes it out, then you lower the water, the ink gets heavy again - It's a royal pain in the butt. But if you add additional coverage in line with those logos, in the same blue, you can keep your ink flowing and water at a normal level. Ink is being taken off and the water now has something reasonable to work around.