I know these tablets are especially formulated and coated to dissolve over a certain period of time. I also notice that all I've seen, quite a lot, are too large to pass through the Pylorus. Do they remain in the stomach for most of their release period, slowly being dissolved layer by layer, and only release a constantly steady small amount of their payload into the small intestine to be absorbed and go to work on the body or mind?
Some extended release products do remain in the stomach while the drug is being released but how they remain in the stomach is often not a function of the size of the tablet itself. To help explain I have included some background information about drug formulation. I am referencing the text, Applied Biopharmaceutics & Pharmacokinetics, and my experience as a pharmacy student.
Another term used to describe extended release products is modified release products, this is differentiated from conventional immediate release products. However, even within immediate release formulations, absorption can be slowed due to the drug itself being in an inactive form or if the drug is very lipophilic resulting in slower absorption by the GI tract itself.
Among modified release products, there are several different types of technologies which provide different mechanisms for slowing the release of drugs or altering the drug release mechanism. Some examples of modified release formulations are delayed release (generally include enteric coated), extended release and orally disintegrating.
Delayed release tablets are sometimes enteric coated. This enteric coat is specifically designed to prevent dissolution of the tablet in the stomach. This is sometimes meant to protect the drug from the acidic environment of the stomach, but also sometimes meant to protect the stomach from the disrupting presence of the drug.
Specifically, extended release refers to a drug formulation where the rate of drug release is engineered by a special coating, membrane infused with the drug, capsule with a special opening, a capsule containing special beads, or difficult to dissolve tablet. Some products use multiple mechanisms to achieve the desired rate of drug release. Referencing your question specifically, there are many drugs that remain in the stomach while the release of the drug takes place but this not true of all extended-release formulations (ex: some drugs are designed to remain in the small intestine). Products that remain in the stomach while the drug is released are known as gastroretentive systems.
There are several designs that have been used to maintain the drug in the stomach. A few of these include but are not limited to high-density systems, floating systems, expandable systems, and mucoadhesive or bioadhesive systems. In the expandable systems, one example being metformin ER, a diabetes drug, the tablet unfolds or expands preventing passage through the pyloric sphincter. These expandable tablets make up only a small portion of gastroretentive products. A more common form being the floating or mucoadhesive systems. In the floating systems, the tablet or capsule is designed to be less dense than the stomach contents and thus remain at the top of the stomach while the drug is released. In the mucoadhesive/bioadhesive formulation, the drug has a special coating that allows it to adhere to the wall of the stomach and prevent it from passing through to the small intestine.
Ultimately there are many technologies that allow for extended release products to function. While the overall concept is the same, how it is achieved can be quite different from drug to drug.