By the way, it's easier if you first plug the battery connector into the board on the phone and THEN position the battery into the battery compartment. This way you'll have the greatest degree of freedom to position the connector for proper insertion.
When you install the new battery, if the compartment is a bit larger than the battery, push the battery over to the side wall and leave about 1mm space between the battery and the electronics. This will give you more room to place the battery cable with the proper twist.
I found that it wasn't at all necessary to remove the front glass. I did need to use a hair dryer to soften the glue holding the battery, but I simply laid the phone down on the face glass and blew the hot dryer on the back for a couple of minutes at almost point blank range. Then I simply held the phone open with one hand, making sure the front glass never went back more than about 80 degrees (no need to stretch it all the way to 90 degrees), and used my other hand to work the spudger around the battery, making sure not to touch any delicate electronics in the area. The top right corner gave away first and then I worked it down from there and the battery came out pretty easily. The trick is to use the hair dryer for a few minutes beyond the phone being too hot to hold in your hand! (you might need to use a towel to pick it up when you pry the battery out.)
Note the long, thin forceps in the photo. These aren't included in every vendor's tool set that ships with the replacement battery and I found it a necessary tool not only for removing this particular plate, but also for positioning the screws back into their holes when you're putting the thing back together. If your replacement kit doesn't include that tool, they're only a couple of bucks and you can get them at any computer geek shop like Micro Center.
It helps if you have fine pointed forceps to remove the thin delicate plate after removing the screws. long pointed forceps also help in placing the screws into their holes when you're putting everything back together at the end.
I found the suction cup to be very effective in removing the front glass. Didn't take that much force to start to see the glass separate from the frame. It's a lot easier if you have a fingernail you can insert when you start to see the glass separate from the frame so that you can let go of the suction cup ring and grab a spudger to pry down one side and then the other.
The method I used was to place the phone on a hard table surface, push the suction cup down so that the bottom is about 1/2" from the top of the Home button, brace the sides of the phone with one hand, pull up on the suction cup ring with the other hand's index and middle fingers while using your thumb and ring finger braced on the table for stability so that you don't pull too hard and rip the ribbon able. It really doesn't take that much force before you start to see the glass start pulling from the frame. As it does pull back, try to stick your finger nail into that crack to hold it open while you grab the pick or spudger and then work your way down one side and then the other.