In Relation to Rebirth After Death, How is Karma any Different than Supernatural gods?
How is karma any different more believable than supernatural gods passing judgement when we are talking about rebirth after the point of death - rebirth being inextricably linked to karma?

The implication here is that death somehow negates the causal nature of mind states that is observed in the present moment; along with our ability to hold grudges from one life to the next, the continuation of physical changes effected by mental states, etc. 

Karma is more believable than God, because karma is seen to work in this life on many levels - mental changes due to karma, changes to one's physical surrounding due to karma, changes in relationships due to karma, etc. The claim that this all ceases at the moment of death is just a claim. It makes sense from within a physicalist framework, but not from an experiential framework like Buddhism.

I mean no disrespect by this, but gravity is observable whereas being born as a human and then a dog after you die because of unskillful karma is not.

Sure it is... the dog observes that it has been born a dog. How else could it be observed? The mind cannot be observed through physical means, so it's a fault of our instruments, not of the process itself. Certainly not reason to conclude "therefore God".

Why is rebirth in human realm classified as higher when some humans suffer more than some animals and have less of an intellectual ability to reason than dogs or crows?

Classification is a human construct; there is no part of nature that says "humans are better". Generally, it's considered to be more difficult to be born as a human, due to the complexity and sophistication of the organism (opposable thumbs apparently mean a lot; complex brain functions, etc.). It takes specific mind states to be born as specific individuals, e.g. humans with Down syndrome, etc., but they still have much in favour of them over dogs (longer life span, opposable thumbs, a place in human society, etc.)

How are you sure this transition to lower rebirth exists, as in the hell realms which sound like really bad places that physically exist, aside from anecdotal evidence that cannot be observed through experience?

I have no reason to doubt that hell exists; it doesn't seem any less plausible than the fact that this realm exists. It seems reasonable that one's environment changes based on one's state of mind, since that is observable in this life, and it is reasonable to conclude that causality also plays a part in one's continuation after death. I am not sure that hell exists, but it seems reasonable to believe realms of that sort do.

Why does no one support rebirth with any solid evidence, but claim it as a result of karma where karma is portrayed as a natural law?

There have been many attempts to support rebirth with solid evidence, some quite convincing. E.g. the articles on this page:

http://www.medicine.virginia.edu/clinical/departments/psychiatry/sections/cspp/dops/publications-page

There is also the superior form of investigation that is meditation; through simple but dedicated practice, one can for oneself regain memories of past lives, according to Buddhist teachings.


  
  So a bhikkhu who is a beginner and wants to recollect in this way should
  go into solitary retreat on return from his alms round after his meal. Then he
  should attain the four jhānas in succession and emerge from the fourth jhāna as
  basis for direct-knowledge. He should then advert to his most recent act of
  sitting down [for this purpose], next, to the preparation of the seat, to the entry
  into the lodging, to the putting away of the bowl and [outer] robe, to the time of
  eating, to the time of returning from the village, to the time of wandering for alms
  in the village, to the time of entering the village, to the time of setting out from the
  monastery, to the time of paying homage at the shrine terrace and the
  Enlightenment-tree terrace, to the time of washing the bowl, to the time of picking
  up the bowl, to the things done from the time of picking up the bowl back to the
  mouth washing, to the things done in the early morning, to the things done in
  the middle watch, in the first watch. In this way he should advert to all the things
  done during the whole night and day in reverse order.
  While this much, however, is evident even to his normal consciousness, it is
  especially evident to his preliminary-work consciousness. But if anything there
  is not evident, he should again attain the basic jhāna, emerge and advert. By so
  doing it becomes as evident as when a lamp is lit. And so, in reverse order too, he
  should advert to the things done on the second day back, and on the third,
  fourth and fifth day, and in the ten days, and in the fortnight, and as far back as
  a year.
  When by these means he adverts to ten years, twenty years, and so on as far
  back as his own rebirth-linking in this existence, he should advert to the
  mentality-materiality occurring at the moment of death in the preceding existence;
  for a wise bhikkhu is able at the first attempt to remove the rebirth-linking and
  make the mentality-materiality at the death moment his object.
  
  
  -- Vism XII.22-4 (Nyanamoli, trans)