Surname Profiler, here: http://www.nationaltrustnames.org.uk/Surnames.aspx shows Rasey as being in two counties in the south of England west of London, and and no results for Rasay or Raasay, which means that there were fewer than 100 people by those surnames in England, Scotland and Wales in 1998.

There is the possibility of what the genetic genealogists delicately call a non-paternal event, or NPE, that is, a misattributed fatherhood. This is estimated to have occurred in 3.7 to 4% of births in Europe and America. (Some say 1.27%, others as high as 10%, but 4% seems to be accepted by most.) One out of 25 may seem like a small number, but over the generations the probability of one have occurred increases with each generation until at 17 generations (or 425 or so years, assuming 25 years per generation) it becomes more likely than not (that is, it exceeds 50% probability) that an NPE has occurred.

Here is the formula and how it was used to determine the likelihood of an NPE within the last 25 generations:

"The proper formula to be followed in this situation (according to the mathematical law of unions of independent events) is: P(robability) = 1-[0.96]^25. When we solve this equation, we find that P=0.64, or just about 64%. See, you have to figure out what the chances are of an NPE not happening in any given generation (in this case, 96%). You then multiply that 0.96 by itself 25 times (to reflect 25 generations, represented here by 0.96 to the 25th power). Finally, you subtract that number from one, because it's actually the inverse, or complement, of the probability of the event's never happening (all probability pairings of occurrence/non-occurrence must equal 1.0).

So after 25 generations, there is 64% chance of one or more non-paternal events occurring."

It may be disappointing that the DNA does not support the paper trail, but genealogical research is like that, and if we prefer fact to fiction we must follow it wherever it takes us.

If I were you, I would go back and look at every point in the patrilineal line to see where the NPE could have occurred. If the test was done at Family Tree DNA, or if you enter the resutls at www.ysearch.org, the results will show the surnames of the men you are most closely related to. This may be a clue. You could then look for a man or men by that surname who were on the scene when each of your patrilineal ancestors was conceived.

True, it may be disappointing to not have the ancestors you thought you had, but on the other hand this is where genealogy gets juicy and interesting, doing original research to discover things no one knew previously.

As to the "fabrication by a preacher," could it have been the custom at that time and place for foundlings to be left on the church door? It's time for detective work.