How to repair leaking blower / air exchanger in attic

Earlier this summer I went up into my attic to retrieve something, and was surprised to feel a cool draft. I discovered that a gap had developed between two portions of the big metal box that distributes cold (or hot) air throughout my house. (This box apparently contains both the blower, and the gas heater.) From the first picture below, you can see that a wire-mesh fabric had been pasted down with this white stuff that eventually cured to form a seal. But over time the seal here broke. In fact, it looks like some settling may have occurred, and the unit shifted about a centimeter to the right. (This is at what I'll call the "far left end" of the air exchanger.)

This was installed about 2 years ago, when my previous unit died. The installers placed it on some styrofoam blocks, which are themselves sitting on a sheet of plywood. However, at the far right– the opposite end from the broken seal– they missed the plywood; there the styrofoam blocks are sitting on top of blown-in insulation, which is pretty much worthless as a foundation. (See second picture.) However, this overhang of weight is so small– it itself is just a styrofoam duct junction– that I doubt that it caused the shift. (There are styrofoam blocks every 12 inches or so for the entire length of the unit.)

So, my question is: is this something that an inexperienced DIYer should tackle, or is there any reason why it would be best left to a professional? And if it is reasonable to DIY, what is that white material that failed? Should I buy more of it, or go with something else?