The third problem is the fact that there are witnesses. God may have performed miracles incognito but these miracles were witnessed.
And I'd like to add another to your list: namely, that many people cannot see the forest for the trees.
For example, DNA is a "tree." Information in the cosmos - both in relation to living things (e.g. DNA and language) and non-living things (e.g. physical laws and constants) - is a "forest."
Another example of a "tree" is self-organizing complexity in nature. The "forest" is that order cannot rise from chaos in an unguided physical system. Period. There are always guides to the system. Even at the root, the atheist must admit that space/time, physical causation and physical laws are guides to the system.
There is no physical origin for space/time and therefore physical causation.
Another example of a "tree" is randomness - stochastic methods are highly effective in physical sciences. The "forest" is that one cannot say something is random in the system when he doesn't know what the system "is."
The number and types of dimensions (spatial, temporal) are both unknown and unknowable.
To put it another way, an observer may look at a "tree" and conclude it is not a miracle. But if he could see the "forest" - he probably would call it a miracle.
True.. Now.. but may not be true in the future.. for some..
Or possibly partially knowable.. There could be dimensions(realms) "we" will never know..
Micro and Macro Universes are even possible..
The possibilies (of what can/could be) are endless..