Those cages should work Cuda, look at the vertical cage on my Wedge, that's tight, but I still can get a small bottle in and out while riding
Please excuse the season of winter commutings grime on the bike
As suggested, maybe look for those side entry cages.
Here is a Bontrager that would look great with your Flyte
I googled it
Here
That or get a Camelbak Mule...

I just picked one up for MTB'ing