On a budget, just get the longest physical focal length you can get. Your 70D gives you a lot of play room with higher ISO to ensure fast shutters so you can withstand apertures around F8 and and ISO 1600~3200 without too much of an issue. If you're shooting from a mount, like a gimbal/tripod, you can get away with even lower shutter speeds.
I would look at the Tamron & Sigma 600mm options to start. They are inexpensive for the raw focal length and optically quite good. For stationary wildlife in general, they really do deliver. See their respective threads for samples. This would be the $1k to $2k option.
Alternatively, if budget really allows, there are things like the Sigma 120-300 which is something I'd consider, if you're interested in getting fast glass and have TC options that still get you to 600mm with great quality without slowing it down too much. This would be the $4k option.
After that, it just goes through the roof, but the 300 F2.8L (even an old one) is a solid choice (600 F5.6 with 2.0x TC and still good), or even a 400 F4L (with a 1.4x TC is quite good still). Or you can hunt for a 500 F4L (old one) if budget is high.
Other options are the old Tokina 300 F2.8 ATX options (if you can find one), or even Sigma's older 500 F4.5.
Know this: you'll never have enough reach. Ever. So learning your subjects is key. I have a mobile pop-up blind that I use. Go out early where you want to be, facing the direction you want to be with respect to the sun so that you're not always back-lit (sun to your back is best for birding), with the gear you need to sit still in a blind for a while. Your targets will come to you. And they will hang out long enough for a few shots. I do this from 10 feet away in a blind with song birds in my backyard. I can get so close that I have to actually back up to 350mm like I did today from 600mm because I was too close for a song bird. Out in the local swamps, I take a blind, and I just camp out for a while. You'd be surprised how much action there is if you just sit and wait (I do so with a stiff pipe and a cold drink in my blind).