Should you continue to pay credit cards monthly if you have room in your budget?

I have a substantial amount of credit card debt, around 60k for me and 20k for my wife. I'm not behind and not being bothered by creditors. I have always made payments on time. Most months I can make more than the minimum payment as long as nothing else creeps up. I've been able to knock it down some. If I stick to my plan I can knock it out in less than 3 years. Most months we stick to the plan unless something like car repairs or right now a new baby comes into play.

Would it make sense to try to settle this debt instead of working through my plan which gets pushed back every time something comes along. I can come up with 30 to 50k if I need to from 401k loans or cash outs to offer as settlement. While I don't really want to hurt my credit it does not seem to matter as every time I pay them down some they lower my limit thereby raising my debt to credit level. At some point I will need to replace my car but can't seem to get a loan due to the high ratio. My credit score is 729 and the only negative is that ratio. I always pay every bill on time but feel I can't get ahead with these credit cards hanging over us. I also don't want necessarily to "take the easy way out". We charged what we charged and I am responsible for it. Just that with interest, it will cost another 20k before we get this done.

Given the above situation, do you have a recommendation?

—Jim