First off, are you sure that your humidistat is working properly?
The goal of this type is to have some liquid reach the bottom of the filter so thatyou don't deposit the minerals onto the filter medium. You don't need a huge volume of water going through it. You might want to temper the flow some. That will help, but not solve the problem. The water should only flow while the fan is on, too, otherwise very little will evaporate, and all of it will go out the drain. Are you sure it turns on and off with the fan? Different brands use different means of switching the water solonoid on and off.
Getting the water to a drain depends somwhat on how far the pump will push it. Usually, they have some minimum head. If you can slope the pipe from the high point, then it should work. my guess is that your joists must run the wrong way if you have to move it that far.
I ran my drain to the washing machine's stand pipe - do you have one of those nearby? Where does your sewer outlet run. Problem is, you'd need a trap, and maybe (probably) a vent to do it right. Is there a bathroom or something above this?
You might be able to put in a drywell, but thatis a little hard this time of year (considering you are worried about ice!). Maybe next year?
I'm not a pro - good luck.