I used the same thick walled rum bottle with a wood topped cork stopper for several years, which was perfect for Cyb’s salt tek. The cork never showed any signs of damage and always sealed nicely. I finally threw it out after leaving a desmanthus soup in it for over a year. I think it matched your description just about perfectly with the exception of it not being flat. I always topped my basic soup up to the shoulder of the bottle and didn’t bother measuring my naphtha, I just filled the neck and kept doing pulls until I didn’t get anything.
The flatter bottle sounds like it might be a good idea for increasing surface contact between the phases, as long as you kept the bottle in some sort of spill containment. Though, I think you’ll get a little more mileage in that regard during the agitation process.
"We dance round in a ring and suppose,
while the secret sits in the middle and knows." Robert Frost