Another option would be to save up for a while and get a body that will balance better with the lens and be a solid upgrade to my t3i overall. I've been considering the 70d, though in reality, it probably makes the most sense for me to simply go full frame.
Congrats on your new baby! One of these days, I hope my needs, desires, and wallet all line up so I can add one to my bag.
Regarding the "balance" of the 2.8 on your Rebel. The grip will help, and a bigger camera (like a 7D, 70D or FF, also with a grip) will help more, but at that weight, nothing really balances well.
With a lens like this, you can't just hold the camera like you could with a smaller lens (both hands on the body). You really need to get used to shooting with your left hand supporting the lens, usually at the foot of the tripod ring. For a better "handle", get a Wimberley P-20 lens plate. It makes the foot of the tripod longer and a bit narrower, so it feels much better to hold for extended periods.
I use a gripped 7D with a 100-400 f/4.5-5.6L IS USM, essentially the same size and weight class as your 70-200 F/2.8 IS USM II. I gave up a long time ago on regular neck straps, and switched to a sling strap. This hangs the camera and lens down at my hip, and is supported by my shoulder, not my neck. I recently switched to an Acratech device that clamps onto the Wimberley plate on the tripod foot, making the lens/camera truly balanced as it hangs upside-down at my hip.
When lenses get this large, you hang the camera from the lens, not the other way around!
The sling allows the camera to quickly slide up the strap and to my eye. Several companies make them. Mine is a Black Rapid.
Enjoy your lens, and get out there & take pictures!