I'd check with your provider, really depends on what kind of switch the landline is on but don't imagine it would have such feature. Though from a technical standpoint it would not be something that hard for a switch to be able to support, so it could very well be some kind of programming option. Whether or not they offer it is a whole other story though.
The relay option, while dirty, would probably work though, if you are familiar with splicing wire and soldiering. Though someone might have a better idea, maybe there's actually a product for that.
Actually one option might be an old school answering machine. Set it to pickup after 1 ring and then plug THAT into the timer. When the answering machine is turned on it will essentially intercept all calls. I don't know what happens if the tape is full though... like if it still intercepts it or not. Never really played with those so not sure if that would even work.