The process of madhyamaka is based on intellectual analysis. Through this process of investigation, one develops insight. This new view is experiential, and this is the point of view of madhyamaka.
After an eon of meditating perhaps. But while one is below the path of seeing one's "insight" is conceptual, and not experiential.
The point of view is either conceptual or not depending upon the meditator.
How long it takes to become the type of meditator for whom it is non-conceptual depends upon the meditator, the methods, the guru etc. Could be aeons could a few years , or months .....days.... really it depends.
You have moved from saying that Madhyamaka is "just an intellectual analysis" to saying that conceptual is not experiential. I would say that for a yogi on the path of preparation meditating with ultimate example clear light, the point of view is technically speaking conceptual, but this means something very very different from "just intellectual analysis," doesn't it? This discussion is about the prasangika point of VIEW, and a view is necessarily experiential, as it is a view.
meditating on a generic image of ultimate truth with a mind of clear light is certainly experiential.
From a Dzogchen point of view, such a samanyārtha (spyi don) is an intellectual analysis, an conceptual contrivance.
Of course, you can play with words if you like, and argue that concepts are experiences, but that is not the distinction that is being drawn here.
The experience of vidyā Longchenpa is referring to is not a samanyārtha, a generic image, even for a commoner. It is also never
a result of conceptual analysis of any kind.
In other words, to tease it out for you further, as you admit, the object for a commoner meditating emptiness according to any system of Madhyamaka is a conceptual object which in truth is conceptual abstraction based on an intellectual analysis.
The "object", for a commoner meditating according to the system of Dzogchen, is always a non-abstract non-conceptual pratyakṣa [mngon gsum] of dharmatā.
The ultimate meaning of both systems is the same, but the means and praxis are quite different -- thus providing the reason why Madhyamaka, being a sutrayāna path, requires three incalculable eons to traverse the paths and stages; whereas the path of atiyoga possesses only a single stage, traversable immediately.