Hi Buddy, just caught up with this thread and you are doing well.
End grain on all timber bodies soaks up more than flat faces and can provide some interesting detailed grain patterns in the overall finish. Basswood typically has fairly shiny looking aspects to the faces which tend to repel stain and personally I stop sanding around 120 to 180 on the stuff to give it a better chance of soaking up some colour. Your choice of selective sanding back and re-applying stain seems to have worked in providing a more even looking colour all over.
In relation to DT, patience needs to be your best friend as it is very fickle stuff to use in hot and humid conditions. If in doubt, best to leave things to cure twice the time you would normally consider as it is so easy to lay a thicker coat than what you may have thought at the time.
Whatever you do, Never use 0000 steel wool to lightly sand back. Andy's advice of a light wet sand with 1500 W & D paper is spot on.
Cheers, Waz