How do you know "there is enough of a signal popping out of the aerial socket in the living room to be satisfactory" if your TV is 15 metres away, & by the time it gets there it's weak? And why should it lose srength in that 15 metre run, if it hasn't lost strength in the run down from the loft?
But assuming you're correct, & the signal is reasonably strong at the socket - your option 3 is a no, no - any such device would be illegal. As for option 1, if you're using reasonable quality co-axial now, it's doubtful if spending more money on cable would resolve the problem. Another option would be to try another booster between the socket & the TV - if the signal out of the socket is, as you say, good quality, then a booster might prevent any further deterioration.
However, the best solution by far is your option 2 - a better aerial - or perhaps it just needs re-aligning.
All the above, however, is on the assumption that you are in a locality where the digital signal is of adequate strength & quality. If you aren't sure put your postcode in UK digital TV reception predictor