I haven't tried the Evernew bottles.

But - I recently changed from using a 2L Camelback inside the pack to using a 1L Platypus Hoser in one of the outside pouches on my pack. I also keep the filter handy (yes - I carry a filter).
So - if getting low on water, I stop for a break (yeah!) and pump some more water.
I've found that taking a break like this actually helps as it forces me to stop and take a break, which gives the rest needed so I can make more mileage.

Anyway - the Platy has pop-tops you can buy, and I haven't had a problem with the hard plastic hose connector, but then it's just 1L of water and it's in an outer pouch.

Doesn't the straw in the Evernew bottle pull up from the bottom of the bottle? That would be my concern with that design...