I think the 6/26 date will probably be ok with a few caveats. The two places to be particularly careful of are the possible cornice on top of the Ten Mile Range which you will hit on day one (Seg. 7 mile 8.0) and the steep sidehill just before Kokymo Pass on Elk Ridge (Segment 9 mile 12.7). There will be sizable group passing through those places a week earlier than you and hopefully (if they make it) they will beat it down a bit. If the sidehill looks too difficult you can probably back up about 2/10 of a mile and go up to the ridge, then follow the crest of the divide down to Kokymo. Be careful if you choose to cross the sidehill and it is still covered with snow. It a long ways down. I would suggest trying to hit that in the afternoon when it will be soft. Postholing would be nice in that situation.
You will probably encounter drifted snow heading into the Holy Cross wilderness, but the problem will not be one of danger, but more an issue of locating the trail. After that, you may find some drifts occasionally in the Collegiate Peaks WA, but they won’t be to hard to negotiate and there will be lots of traffic in there.
You should keep an eye on these forums - someone will likely report on conditions at those places as the season progresses.
bearcreek