You don't want to use an inside flange on 3" pipe.
What you were planning to do is certainly one "right way" to do it -- that is, to remove the old flange and install a new flange mounted on top of the finished floor. A+
However, you are also correct that this will likely be a significant DIY job, and the ways to make it easier (i.e. inside flange) are actually not good solutions.
Accordingly, given what you've got, a straightforward solution would be to use a stainless-steel repair ring to repair the portion of the flange that is cracked (I assume that cracked portion is PVC and that's why we recommend that if folks are going to use a PVC flange that they get one with a stainless ring). Sioux Chief makes one called the "Ringer"; it's a stainless ring that screws onto your old flange. Then, I wouldn't bother raising the flange and would just use two wax rings to form the seal. Get one with a horn and one without. Stack them on the flange as follows: hornless one on the bottom, one with horn on the top so it doesn't slide around, mount toilet on top and compress carefully and straight down, and you're set.
We also don't recommend flange extensions that go on top of the flange, because they are more prone to leak than a stack of two wax rings.
Oh, and when you are installing the toilet with closet bolts, get a brass closet bolt set that has two washers and two nuts per bolt. Use the first washer and nut to secure the closet bolt to the flange, and the second washer and bolt to secure the toilet to the flange. That's our recommended way, and it makes for a nice firm connection all around.