This has been interesting to read, and there has been a lot of good advice.
One thing that I would suggest is showing pics of the body to Adam. The cost of return is high, but he may give you a discount on something to offset the poor quality of the body. One thing I would suggest if you purchase one in the future is to ask Adam to take a look at what they send you before you get it. This won't catch everything, but would probably have caught whatever is going on with the horn.
Australians can send their kits back for free, I think, so the "check" is not as necessary, but he's been willing to do it for kits that go overseas. From hard experience I can tell you that the US kit suppliers and even high end suppliers like Warmoth will make you eat return shipping, and they typically will not go to the trouble of checking what they send before it goes in the mail.
Couple of thoughts about the finish. I think what Simon says about basswood is mostly true, but YMMV. This is a basswood back on an ES style bass:
Attachment 42447
I liked it so well that I just sanded lightly and clearcoated. I have also seen basswood with almost no figuring.
I also have a Fender Coronado with an Antigua finish. I have read that it was probably intended to be a "wildwood" top and back, but on some the glue used to attach binding stained the wood so that they could not finish clear. for that reason they developed the weird solid color burst. Ever since I have wondered how many solid color Fenders (and others) started off with clear. Not sure about this, but I can say with certainty that you can find a failed stain attempt under one of my builds ;-) I also have one successful stain as well where I had already picked out the solid color for if I botched the stain job.
On your build, it would be interesting to see what the "flaw" will look like if you do stain it. The conventional wisdom is that it's a flaw, and the conventional wisdom is usually right. If it sucks you can always paint a solid color.
On the other hand, I have a PB neck with an eye in it (not a birds eye). This would generally be considered a flaw, albeit one that does not affect the stability of the wood. I finished it clear anyway. I was pleasantly surprised by the chatoyancy it developed. It actually looks really cool.