connect 3 inch ABS pipe to only 0.5 inch exposed pipe
No, it is not. If you read the manufacturers' instruction on the ABS cement it says to seat the pipe completely in the hub.

Now... I have cheated the above instruction on more than one occasion but never to that extent. If you are careful, gluing to 1/2" of pipe will probably not leak immediately. The problem is that the strength of the joint will be compromised and any movement (due to soil movement, expansion/contraction of pipe with temp changes, etc.) could cause failure.

I say you should "bite the bullet" and cut back to the next available spot where you have some pipe to work with. You will likely have to rebuild that whole junction area.