Most parks in the Tulsa District enforce the 14 day rule. There are enough parks, often several on the same property, that you can move easily from park to park. Only working volunteers stay longer.
These properties remain in high demand every weekend during the season they are open, and on weekdays for the height of the season when schools is out. The CoE parks represent the greater part of the camping opportunities in the area covered by this District, so local management is less likely to be liberal with the 14 day rule.
Some city/county parks, tribal parks, and state parks off season, operating parks on Corps property, allow longer stays. So does at least one concessionaire, who has some residents who have been there for more than ten years continuously in his "fishing camp." But when someone else is operating on Corps property, it is no longer a Corps park, so rules for operation of Corps parks do not really apply.
FWIW the 14 day rule comes from an Army regulation. It is up to the local command to interpret and enforce it. Enforcement is variable, I would not count on lax enforcement for travel planning purposes, but if you find what suits you at one location, stay there. Another rule in the regulation says you must occupy the site, sleep on it, to keep it. The campground I use most lets people put a child's play tent on a site for up to two weeks before the weekend they actually want to use it, so long as they are paying the fee. This grates with me, when I come in and can't camp midweek because all the sites are "occupied" though not being used, but I also understand that this revenue is what keeps the facility open.