The snow cups were a real pain to get off, though, so I was expecting this to be even more difficult
Hmmm ... I surprised to hear you say that since the Komperdells I've seen use two opposing tabs to hold the basket on, and a quarter turn will pop them off. Leki tips use a screw-on type of basket, so you might need to spring for a new set of baskets. If you have to - look at Black Diamonds - they are cheaper/better than Lekis IMO.
Kevin