Do you believe the government and medical complex are incapable of putting a reverse transcription into the vaccine on purpose and lying about it?

They absolutely could. Its not as simple as just adding that enzyme, but yes, they could put all the machinery in with the mRNA. There are a few reasons why I don't think they did.

1. They want to test the technology as advertised. It's actually pretty cool tech, with potential applications. The problem is, its originally a cancer tech. In order to get large scale testing there aren't enough cancer patients (of the type this tech could be used on). They need another application, like an emergency vaccine.
2. There are better ways to alter DNA than the method suggested. CRISPR-cas9 is WAAAAYYYY better, if that was the desire.
3. There is no reason to alter our cells to permanantly produce THIS particular protein. There are much better proteins for many different purposes that would be much more interesting.
4. They woud be found out (eventually) if they put in other ingredients than what is listed. They are currently completely free from responsibility with regards to this tech. But if they put something in that wasn't listed, they could be sued for all their worth. They would lose everything.

Would people who happily make chimera human mice have reservations stopping them from altering human dna?

I do not think the PTB have any moral qualms about doing such a thing. I think it is likely that that is a goal. I just don't think they are doing it with this.