Well I expect even the religious, can work out the problem with this........ 
People have many different ideas of God in their head and in some ways they conflict, even within the same religion.
If God who was greater and perfect put it there, in people's heads, then there wouldn't be so much arguing and strife and morons like Isis wouldn't exist.
The assertion that you can't imagine greater, is rubbish, I see no evidence for this......and to draw the conclusion God exists because of it, is nonsense and doesn't logically follow.
That is if you can twist your brain round the convoluted. argument he makes. ( or maybe because I've got the lergy, too many bloomin colds / sort throats about 😷)
The guy thought too hard and needed to be given something more practical to do, IMO
Firstly, what you have quoted in your post is the ontological argument but what I have presented in the OP is a step on from that; if you like ontological argument 2.0 (OA 2.0).
As I have said elsewhere on this thread and others God is just a word and could be replaced by the word "Something", and as such, because man is not perfect, his thinking beyond what is natural and beyond his experience will create imperfect 'images' which will not only conflict with others' ideas but with himself.
But my point with you has not been on this issue (OA 1.0) but on the fact that we humans do think beyond our natural conditions and experiences and as such this can't be explained by these natural conditions. This is what OA 2.0 says, that the lesser (natural experiences and conditions) can not give rise to our imagination's fantasies etc. which are 'above' the lesser conditions of our natural experiences. So how do we explain and give an account of how we have such an supranatural imaginational function?
Let me give you an example. If we have a sculptor in stone of a figure and it gradually over time erodes away into dust then that would be seen as natural; in effect the greater giving rise to the lesser - a created form going into an entropy of a pile of dust. This can be explained by natural means as it is a possible aspect of our experiences of our lives. However, if the reverse occurred this would be seen as supernormal. A pile of dust gradually forming together into a perfect intelligible stone figure. A lesser producing a greater. This would need an explanation beyond what was available to the natural order of things, and much more than what you have offered of the like, "Well, I've seen it happen, it just managed to come about." The same is true of our imaginations as they create much more than what is seen in the world of our experiences and as such must be the product of "Something" greater than our natural experiences of life on Earth.