L.B.
Well I can't say there is a magic way to make it work, but one of my favorite sippy cups were the Nubs or maybe Nubbies at Walmart (can't remember the actual name but that's close...they are usually on a bottom shelf under all the other name brand sippies and in a bin)...they were colored (which made them fun) and the tops were the silcone just like what you would have in the top of the bottle. There were 2 kinds...one was a sports type bottle which had a mouth piece that was VERY similar to a bottle...my recommendation would be to try that one first. The others have mouth pieces just like the other sippies but they are ALL silicone which makes them very similar to bottles and easier on their mouths.
The up side to these sippies is that they are very economical...the downside is because they are so economical the brand won't make replacement nipples/tops for the cups. So if your daughter starts teething on it and chewing eventually you'll just have to toss the whole cup out b/c there is no replacement tops for them.
As for the other harder lipped sippies...I would certainly hold on to them. I don't think we actually started using the valves on those until 15-18 mos in my house...sometimes the valves are just too hard of a concept for them. Also, after they started chewing on them it made them even less desirable because the plastic fragmented and was rough on their lips. Hope this helps...best of luck to you.