WHh wouldn't they slow down and beam in some debris in hopes of getting a hint about the "enormous power" enemy weapon? If they didn't do it, they'd be negligent.
Good point, apparently they could track the Romulan ship and still collect some samples. Had the visual scanning range ever been established in comparison to the transporter range?
Another point suggesting warp drive capability, IMHO, is the opening dialogue of BoT which I think we didn't examine last year:
SPOCK [OC]: Still no answer from Earth Outpost number 2, Captain, and now number 3's gone silent.
KIRK: Maintain course to Outpost 4. Keep me informed. Kirk out.
SPOCK [OC]: Earth Outpost 4 reports they're under attack. A space vessel, identity unknown.
Considering it took the Romulan ship apparently at least several minutes to reload, the Enterprise was obviously not in permanent touch with Outpost 3.
Yet, I guess it's fair to assume that the outposts were separated by plenty of space between them.