If it were my job, I would use the grade beam, but there is a good chance that gravel fill plus concrete cap will be OK if the addition stays 3-5' away from the tank. Of course, if it were my job, I wouldn't be hiring a contractor, I would do it myself. My philosophy has always been that I would rather spend $500 on extra concrete and steel than spend $500 on engineering to prove I didn't need the concrete and steel.
There is a another area of non-compacted earth you should be aware of, and that is the backfill around the existing tank.
When the tank was installed, they dug a hole which was bigger than the tank, probably ~12" clearance on all sides, put the tank in, and then backfilled. It is almost impossible to compact that backfill, and in most situations it doesn't really matter. Over the years, it settles some, but it is never, ever, going to reach full compaction. Put a force on that soil in a new way, and it will settle some more.
The problem with building on unstable soils, and this soil is unstable, even if the rest of the property is stable, is that settlement issues frequently don't show up for years. In most states, a contractor is liable for his work for one year. By the time settlement shows up, he is no longer liable, if you can even find him. In fact, a lot of contractors build something, see that it is OK for a few months, and then go away thinking they have built something which was just fine.