1. Is there any mechanism that would allow HGT to take place between relatively complex species without the action of an intermediary, as you describe?
Not that I know of.
2. What happens to those gene fragments in translation? Do they end up in the same place in the genome of the last species in this chain as they were in the first?
Extremely unlikely.
3. Could this happen with anything like the frequency necessary to account for all the exact ERV correspondences we see between, say, humans and chimps?
Extremely unlikely. And as noted in 2, even if they occurred with sufficient regularity they'd be in the wrong places.