I used to deliver appliances, and we used the self-piercing saddle valves for years without any call backs, but I can't say how they do after 6 or 7 years. I can say it's a lot easier to use one, but I too have heard several times not to use one as of late.
Steve's right; a plumber may be in order here unless you're real good at brazing copper, (I'm not).
I answered another post in the last 2 or 3 weeks about icelines and how to connect the copper, leaving lots of coils and securing the line at the baseboard and on the fridge frame with clamps, to secure the copper where the compression fittings are. Use Ctrl-F on the main board and look up the word "line" and see if that gets you there.