Intense competition with Belzoni? Belzoni was there years before and Vyse easily surpassed what Belzoni had done.
Desperate need of a significant discovery? What need? Who do you imagine Vyse was answerable to? Vyse and Perring provided the best architectural account of the pyramids to date and for a long time after. There were plenty of significant discoveries.
Obsession with firing Caviglia? Vyse had no need to hire Caviglia in the first place, other than his being persuaded that Caviglia was the right man for the job. Caviglia proved not to be.
Late-night secrecy? What is this nonsense? Look at the chambers: you’re not going to get a football crown in there. Numbers were limited of physical necessity and there were dangerous things going on: blasting and removal of debris. Even so, Vyse did invite more than a few people to come and see. More Sitchin mythology.
The gunpowder thing is tired. Standards were very, very different then and technology limited. Belzoni’s methods were scarcely any better, yet we rarely find Belzoni condemned to anything like the same extent.
I suggest you attempt to systematically question and purge your mind of all of the factoids on this question which come (most of them) ultimately from Sitchin’s myth-making.