Which tensioner - the spring-hydraulic or the cassette? Better be the cassette for that cost (R&R the engine).
What are the symptoms (noises and or performance issues and under what conditions do they occur and when were they first noticed)?
If the diagnosis from he dealer is correct (assuming cassette or boondoggle), to me, it becomes a question of economics - to repair or replace the vehicle with new or used. You have an 11 year old vehicle with unspecified number of miles and unspecified maintenance; there are certainly a few age-related problems lurking (i.e., body mounts, suspension bushings, etc.) that shouldn't be significant considering the age, but a consideration. $2800 for a few new parts and a bunch of labor or another $2400 for a bunch of new and reconditioned parts and about the same labor.
What warranty is provided with each option?
How long do you plan on keeping it?
FYI on rear timing chain cassette replacement:
