When it comes to towing, it is all about weight, less about size...
- This is where RV designs come in handy. Thin framing, paneling and foams. They are stronger than you think, when combined. Some even stronger than typical "heavy", but "cheap", home designs.
When it comes to "living", it is all about "comfort", less about traveling...
- You don't expect to live in a car, and shouldn't expect to do daily traveling while towing a load. Unless that is your only option. Still, you will be doing less time traveling than parking and sitting in comfort. Not being able to do 75-85 on a highway is not a bad thing. Only getting 8-12mpg is not a bad thing either, if you are not driving all over creation, towing your home with you. If it is that big of a deal, pay to have it towed with another vehicle. They do have one-way towing services that are affordable for long journeys. (That is what most tiny-homes use for mobility between locations, instead of having to buy a double-axle truck, just to tow, which is a nightmare as a daily traveling vehicle.)
- In a pinch, even a smart car can tow a 12,000 lb (6-ton) load. Just not fast... and it would need to be "balanced" well. Again, it should not be a daily event, driving around without a destination in mind.
Honestly, a large permanent-set/stationary "mattress bed" is a luxury...
- Luxury, as in, it would often have a whole room dedicated to it, in a house, AKA: "Bed room".
- You now live in a "Studio apartment", and have to design for that.
If you have to compromise on anything, it should be the things you use/do the least.
- Standing (You don't do it as often as you think)
- Cooking (Maybe an hour out of your day, total) {Waiting for something to cook doesn't count} *
- Showering/Potty (Maybe an hour out of your day, total) *
- Getting dressed (1-5 minutes... {Avoiding the sexist joke here}) *
* All these can be done sitting-down, which most actually do, in transition or while waiting, without realizing it.
The majority of your time is spent doing these things... (Normally, individually, not combined)
- Sleeping (6-10 hours)
- Sitting {work/entertainment/driving} (6-10 hours)
- Walking/standing around inside/outside (30 min - 4 hours) {Walking around inside is not done often, if it only takes ten steps to get across your whole house. You walk in a big house, because it is big!}
People don't usually just stand around in houses, they sit. However, there are certain things we normally do standing. (Showering, cooking, getting dressed.) Though, those can all be done while sitting. Ask anyone in a wheel-chair. It is not any less comfortable. For those not in a "wheel chair", you usually would find them in a rolling computer chair. (Just not in the shower. Though, sitting while showering will reduce your chances of an accident by nearly 800%, where most home accidents happen.)
You can get a decent "pop-up" or "dome" or "extension", to create a special standing area, if something isn't as tall as you want it to be. They are not difficult to install and are quite rock-solid in design. Though, it would be better to just get something as tall as you need, if you "need" that.
For more room, you can exclude a "stationary bed", with a few designs...
1: A fold-up "Murphy bed"
2: A a hide-away "Day bed"
3: A dual-use "Couch bed" or "Table bed"
4: A rigid hammock **
A Murphy bed can act as extra insulation on your hottest wall, or coldest... Pre-warmer in winter or pre-cooler in the summer time. The design can also use the under-space as storage, seating, or lift-up wall-racks. Combining use or constraining wasted space.
A Day bed can also be a couch-bed that simply gets larger. However, it can be completely tucked away under counter-space, if you want it to occupy space that you don't use while sleeping. (The main walking/standing area.)
A Couch bed, or Table bed, commonly found in RV trailers, would simply convert directly into a couch or dining-area, when not in use.
A hammock is awesome for winter and summer. Because in the summer, you can sleep near the cool floor and are not sleeping on a bail of insulation. In the winter, you can rise-up to the trapped heat, away from the cold floor.
** There is a fifth bed setup, but that requires a TALL trailer, which you indicate is a limit you would rather save for "walking/standing". That would be a winch-bed. The bed would raise up to the roof, so you could access everything underneath. More ideal for tall "tiny homes". This can also be done with the Hammock, instead of one that you would normally disconnect and connect manually.
