As noted earlier, tantra uses an indirect method with deity yoga and the channels to reach buddha-nature, while Mahamudra goes there directly. .
This completely false. You really have no idea what you are talking about now. In Vajrayāna, pointing out the nature of the mind, the all-basis (ālaya) and recognizing it, is the foundation for creation and completion stage practice. Mahāmudra is not just the nature of the mind.
If it were as you say, we would have examples of Indian Mahāsiddhas who attained buddhahood on the basis of merely meeting someone and having a discussion, but we don't, training gradually in ṡ́amatha and vipaśyāna.
What we do have are examples of mahāsiddhas, very many in fact, who attained awakening and realized mahāmudra during the process of receiving the four empowerments. We have many other examples of mahāsiddhas who, having received the four empowerments, practiced the two stages and swiftly realized mahāmudra and so attained buddhahood. We have no examples of any Indian mahāsiddhas who did either based on a mere conversation, or through merely practicing śamtha and vipaśyāna, whether sprinkled with pithy saying from the dohas or not.
So I guess, Tibetans must have much higher capacity than Indians, because according to you, these vaunted Tibetans are capable of realizing Mahāmudra based on sutrayāna conversations, sprinkled with dohas, merely practicing śamatha and vipaśyāna. But the reality is, no one realized mahāmudra without practicing the two stages, including Gampopa.
Also, the fourth empowerment is generally equated with the pointing out instruction
Which pointing out instruction? Whose? What precise text? If you intend the means of pointing the "sūtra" mahāmudra system, for example, in Bokar Rinpoche's famous condensation of the 7th Karmapa's long Mahāmudra text, this is in no way shape or form equivalent with the fourth empowerment.
As above, the specialty of Gampopa's Mahamudra is the direct introduction without empowerment.
It is not a direct introduction, it is a gradual introduction, that takes many sessions, like all sutra-based systems. You yourself admitted that Gampopa's "mahāmudra" was "sutra" mahāmudra.
Now, when it comes to essence mahāmudra, there is an empowerment (the descent of the wisdom vajra empowerment) based in Indrabhuti's famous text, the Jñānasiddhi, and this is in fact a direct introduction, just like the fourth empowerment.
All I can conclude from this discussion, Astus, is that you are not really very clear on the difference between "pointing out instructions", which is gradual, and "direct introduction," which is immediate.
Further, what you seem to fail to understand is that in actual practice, in general the Kagyus all practice creation and completion stage, combine the four yogas of mahāmudra with the completion stage, and practice the main practice of essence mahāmudra, Guru Yoga.