One reason we are not allowed to "return" a cooked food (in a pot) to the fire on Shabbos is that it "looks like" you are cooking. ("mechzei c'mevashel"). This makes it forbidden D'Rabbanan.
However, D'Oraisa (Biblically) once a food has been completely cooked, it cannot be cooked again (ain bishul achar bishul) unless it is a liquid that has completely cooled down.
We can place a "blech" (simple sheet of metal to cover/retard the flame) on a stove top burner, before Shabbos. This causes two things to happen:
Putting fully cooked food on such a blech, no longer "looks like" cooking, because no one usually wants to cook on top of a retarded flame.
A blech is viewed by the Chazon Ish as one sheet of flame. However, other poskim accept the concept that a blech on a stovetop has zones (on the fire, yad soledes, not yad soledes ). One ramification is that putting food on a merely "warm" spot can help heat up the food but still be distant from questions of cooking.
The oven however runs into potential problems that the stove top doesn't have to deal with.
1.) Although there is no bishul after bishul, there can be baking after bishul. If a type of cooking is different from how the food was prepared the first time, it may be considered cooking anew on Shabbos. Ovens bake. Pots on a stove cook. So putting dry solids that were boiled in a pot within an oven, would raise the idea that they are being "baked" for the first time on Shabbos.
2.) Many try to avoid opening an oven door on Shabbos if it will directly affect the thermostat and cause an increase in fuel consumption to automatically turn up the heat to compensate for the new cold air rushing in. Similar to opening a fridge on shabbos, this question is a subject of dispute between R' Moshe Feinstein Z"tzl and R' Shlomo Zalman Auerbach Z"tzl. R' Moshe is machmir since the new air is "your force" while R' S.Z. holds that you merely removed a shield and the air flow is not "your force".
3.) Everywhere within a modern hot oven, is one uniform temperature, and the flame is not retarded by a blech. Therefore, using the oven in a regular manner, always "looks like" cooking.
In ancient times, a blech was possible within an oven by scraping out the coals and sprinkling ashes over the flame. Nowadays, there is no such thing.
4.) Sometimes, you can cause a modern oven's lights to turn on when you open the door.
That also explains why the authorities quoted by the OP says: "that one can use a "warming drawer" if it is lined with foil and the nobs are covered."
The lining and knob covering, create a "blech" for the warmer's heat source within. Not everyone holds you need to cover knobs or gas range dials. The lining is the main thing since that is what retards the flame and makes it not the normal way of heating food. The knob cover is an added reminder not to play with the heat levels on Shabbos. However, once one has "removed their mind" from the fire by covering the heat, the knobs should not matter according to the lenient ones.
So probably, a way to use the oven on Shabbos would be to take dry solid baked chicken, rely on R' Shlomo Zalman to open the door, and/or use a type of modern oven that has a Shabbos friendly thermostat, and electric lighting program, and somehow create an insert within the oven that you can place food into, which seems to block the heat from fully penetrating the insert.
If you can do all of that.... it seems OK.
I hope this helps. :)
