As for a strategy to overcome this, it seems like that you're using only one strategy which is based on completing a long route, with overlapping tickets, as the main method to gain points.
Something you may be missing is that if your tickets are only short routes, you can finish them easily and them spend the rest of the time doing two things:
- Claiming 6 train routes
- Preventing your opponents from completing tickets.
Something to try next time might be then to start on your hardest route, but watch for a clear destination from an opponent. Then spend some time blocking him. There are a few key routes that are not only worth points, but also are hard to go around. You will need to pay attention to which colors your opponents are collection as well as where they're building their trains, so it is a more difficult strategy to pull-off, but it can work well. I've seen several games where the only people to complete routes were people with small ones, and therefore the small routes tickets won.
Since you also asked for an alternate house-rule, one that adds fun is to draft the starting cards. Everyone draws three, picks one, passes the rest left, then people pick one of the remaining two and discards (face-down) the last one. You get to select from more cards (2 of 5) but you also get an inkling of what your opponent(s) may have.