You can switch to co-wash (only conditioner) and see if that helps. There are various levels of this, from every day to once a week. You can use just water every day or every other day if you go once a week.

You can also use heavier oils in your hair for a week or two, still shampooing every few days, and just replenishing with heavy oils after. To get through your "two weeks of oily hair".

What is happening with a constantly scrubbed scalp, is that it is always in crisis mode. It is sensing it is completely free of oil and producing large amounts of oil to compensate. This is not only too much oil, but it is quickly produced, substandard, emergency oil.

You need to convince your scalp that it is safe, and that it can go back to producing smaller amounts of higher quality oil. This also means that after you get things right, when you do wash, you put some oil back in. This will keep it from going back into crisis mode.

If you can't roll around with super oily hair for two weeks, which is understandable, you can slowly try to get your scalp into this state, using limited washing, co-washing, and oil replenishment.