I thought someone would answer you before now.
that is only two coats:
The Watco Teak oil says to flood the surface, let it sit for 30 minutes, then wipe it dry.
Reapply and soak for another 15 minutes and wipe it dry.
Ready to use in 8 - 10 hours.
I should also have asked; how old is the wood slab and how long
has it been processed into a slab. (is the moisture content known).
here is my concern:
over the course of a week, you applied dozens of coats which soaked up two quarts
worth of Watco Teak oil. the instructions state 2-3 coats "should be" sufficient.
if the wood is in extreme distress, 4-6 coats may be required, 12 hours apart.
in my uneducated guess, you have flooded the wood to the point that the inside
will not dry or cure. it is sort of like you have created a skin in a paint can.
the floating skin appears to be solid. but underneath, it is still liquid.
if you google: "teak oil won't dry" you will find all kinds documentations of the
same issue. and most are different with the type of wood they used.
not to drag this out, but, I think you applied way too many coats in too short
of a time period. continually wiping the surface with a solvent such as mineral spirits,
naphtha or xylene "could" remove the surface oil and let more fresh oil rise to the
surface. but, I have no idea how long it would take before it is "dry to the touch".
I would suggest you call the Watco help line listed on the can for assistance
right from the source. and explain in detail, the type of wood, moisture content,
the climatic conditions of when you applied it.
years ago, I had a very similar issue with varnish. I called the help desk.
the technician said I had "vehicle entrapment". which is what I explained up top.
the skin dries, trapping the fluid inside the wood. I used some pretty extreme
measures with hot solvents to get the project back on track.
maybe one of the Chemical Engineers will be along soon to provide more
possibilities of how to correct your issues.