Hey HF, i myself have recently run into this. Ive been using my method to boost during the hot, arid summer days of texas, where i would notice the thick goop would dry enough to where i could slather glue onto the rubber/blade and be done.
Now, with winter weather heading our way, ive run into the same problem as you, but i may have a solution. Before i mention how i am tackling removing this goop build up that just wont dry, let me first say DONT TRY TO GLUE THEM ON YET! you are correct, it wont stick because the oil wont let the glue dry. this is the problem ive run into with the big dippers (its not that they are domed too much, its the oil/glue layer is keeping the rubber from sticking because the glue wont dry, even though the layer itself is extremely sticky).
So how do you remove this layer? Masking tape. Take a strip to the sponge, and peal gently. (When you peal however, make sure you are pulling the tape backwards, not upwards). Do this enough times and the back will look much dryer. This should allow the rubber to dry enough (may take more than a week, or a few days).
http://imgur.com/a/IJTs9
Be extra careful with softer sponges, as they tend to rip! i have have managed to remove quite a bit of this goop layer. I will be attempting to rettach my big dippers soon!