Well, there are various strains of Gelug thinking. But in general Gelugpas strenously defend the idea that the intellectual exercise of identifying the object of negation, non-affirming negation, the emptiness of true existence in things, the negation of inherent existence resembles the actual realization of emptiness, is it is appropriate to be maintained conceptually.
, yes. It gets you barking up the right tree, so to speak.
I'm extending myself a little here beyond what I've been specifically told, but in terms of maintaining
the position, it seems to dovetail nicely with the Sutrayana Mahamudra. Anything that they can focus their attention on is taken apart in search of its essence, etc. But as you say;
Granted, the Gelugpas also wish to go beyond mind
...but they spend a lot of time defending and insisting that one needs to have a perfect Madhyamaka view before moving on the Vajrayāna
No argument there!
...and insist that one needs to continue to cultivate that view.
Well they certainly do not embrace any other views.
I have been taught that the "84,000 teachings" are organized in the same way that a dog trainer trains a dog to sniff out drugs or explosives. How do they do that? They take a ball and play fetch. The dog is already hardwired to do that, no training needed. Then they take the next step, where they hide the ball. "Go find it". The dog plays the game, sniffs around, and finds the ball. Then they fill the ball with drugs. The dog sniffs around, then finds the ball which also smells of drugs. The next step is the trainer stops hiding the ball, and just hides drugs. The dog is now habituated to sniffing out the drugs. It is still playing the same game.
In terms of how the Dharma trains us like we train dogs, it takes what is already going on with us and then directs it to Dharma. If we have a negative mind that is intolerant, then we are given the Pratimoksha Vows. If we're going to be uptight and say "no" to things, let us say no to the bad things. It is like a double negative. So the negative rule-bound mind is brought to Dharma and is ultimately resolved
in it. That is why the monk's vows are for one life only (as opposed to the bodhisattva vows which are for all future lives).
In terms of the Sutrayana geshe/khenpo programs, the same is true. If you are already intellectualizing Dharma, then bring that tendency fully to Dharma. The Gelug approach is to logically prove that the way things abide cannot be put into a logical proposition. That is resolving
the intellect into Dharma.
Seeing things that way gives the Gelug approach an elegance that I think is missing in the wider discussion of Dharma. The intellect is the wrong tool to approach emptiness. (Just ask a Zen person.) But since that is the tool that we have in our hand, then bring it to Dharma fully, so we can see how to put that tool down. It's not nihilism. It might be if they didn't go on to Vajrayana, but they do, albeit behind a cloak of secrecy.
And I'm saying that as a Shentongpa/Kagyu. It's not my path, but I do appreciate how they go about it, and what they are trying to do.