It’s very difficult to prove a negative, but I am reasonably confident that no rule in 3.5 or Pathfinder explicitly states that all armors of a given weight class slow you down by the same amount. In 3.5, at least, there were certainly a few super-heavy armors that reduced the speed by more than your typical heavy armor (Races of Stone had a couple of these).
So yes, every Medium or Heavy armor must somehow explicitly state its own speed reduction, even if the overwhelming majority of them have the same speed reduction. On the other hand, if a given case failed to do so, I’d just chalk that up to the designers not realizing there was no such general rule, since it usually is so consistent and armors which slow people more or less than others in their category are quite rare. It’s also worth keeping in mind that it is consistently weight category that we should consider, not sheer weight.
Short answer:
No, there are currently no rules about what happens if you sleep in armour.
The are rules about how fast you can don and doff armour [pg. 146 PHB] that's quite kind and fast (you do not don full plate in only ten minutes in real life) so characters shouldn't really have any issues with switching in and out of armour.
The are however rules for swimming in armour. Page 183 in PHB under the heading Suffocating. It's what you use to simulate drowning which is what happens if you try to swim in armour, especially the sort made primarily of metal.
Long answer:
Sleeping in armour while not ideal or the perfect recipe for a great night's rest isn't as bad as you'd think. Anyone who ever played hockey or American football knows that laying down and rest in all that padding and equipment isn't bad.
People all through history have actually slept and spend long times, sometimes months at the time, pretty much constantly wearing armour both day and night. The great siege at of Malta is one such example. Another example though a non-combat one, is how the moon astronauts slept in their space suits during breaks between the moon walks. Even now modern soldiers are sleeping while wearing body armour.
Now some might point out that modern battlefield body armour is designed to be comfortable. But that's just it. All armour through the ages has been designed to be comfortable to wear, to move in and to rest in because otherwise no one would be able to use it during long periods of combat. Full plate is both agile, flexible and feels light to wear.
Second thing to think about is that humans are adaptable and can learn to endure the harshest conditions (can't speak for those poncey elves though). The human brain can actually tune out things it finds annoying or distracting over time. So even if it is uncomfortably to wear armour you forget it after awhile.
Which bring me to my point. (Finally right.)
If the reason you want rules for sleeping in armour is realism you don't really need rules as the effect of a night in armour would be negligible for a fit person trained in wearing armour.
You might give the players a disadvantage for the first roll they make after waking up if they make sleeping in armour a habit.
But the truth is that the cold, wet and fear of sleeping outside in a dangerous situation have much greater impact on how well rested you are than if you sleep in your armour or not.
However, while sleeping in your armour might not be that bad for your rest, prolonged armour use without breaks will eventually lead to all manners of unpleasant side effects. For example there is something called pressure ulcers also known as bedsores. They are incredible painful and nasty. Another nasty effect is spinal compression.
Now there might not be any rules for those effects either though if they were they would most like be in the form of sickness and injury than anything else. Still, Google some images of bed sores and show your players and they might start removing their armour a bit more often.
Best Answer
Short Answer
No, you need 5 minutes to doff plate armor. You could use illusion or possibly transmutation to create the appearance of armor. To persuade your DM to have easy-off armor you might have to pay a real world or game world cost.
Long answer follows..
RAW
The RAW say that Heavy Armor takes 5 minutes to doff (PHB 146), so instant doffing not possible.
You also can't teleport out of it, because as you say you can't cast spells in it.
Illusion
It sounds like you don't actually want to use the armor as armor (you want to take it off as soon as combat begins), so why not just create it as an illusion? As an example, Disguise Self seems to do the trick. It's a first level spell too, so much 'cheaper' than teleport! If you're high enough level to be using seventh-level spell slots then your spell save DC is going to be quite tough to beat (in terms of others seeing through the illusion).
Even so it would take your first action of the combat to dismiss the illusion. However, you could use a Hat of Disguise (DMG 173), and in that case it would just be a case of taking off the hat, a free action:
Transmutation
If you would prefer not to use an illusion, you could use a transmutation spell. For example, you could see if your DM would let you use Alter Self, though the wording of the spell is unclear as to if you can actually create the appearance of armor.
"Clothing and armor" are not mentioned, so your DM would have to rule this one.
Persuading your DM
If you really want to go with armor which falls off quickly (which is a hilarious image!), there are two basic ways to convince your DM:
In any case your DM can put serious limitations on the fake armor, like it's difficult to move in, or one hit and it falls off. Your DM might also refuse outright if it doesn't fit the tone of your campaign.