Camper or caravan with a low roof?

I don't think much of your chances. you could try looking for a Pratline low tow. They are getting a little long in the tooth, I don't think any were made this century - See this link

For something a bit newer you could try an ECO Tourer. Their standard model without shower may scrape in, if it doesn't then you can purchase or construct some storage wheels for it.

You could let some air out of the tyres to reduce the height abit

You can buy small rubber wheels that replace the vans wheels designed purely to lower the height so you can fit them under low roofs etc, caravans plus sell them, you obviously have tho change to your proper wheels once its out of the shed!

One thing I noticed when looking for a camper last year, was that they seem to hold their value. The prices some people were selling them for, was not a lot of difference from buying new. Obviously depending on condition and age.
Have a look at the new ones, then go back in a couple of months. Towards the end of the year, prices seem to go down, or bonuses get to be put on. Showing cash also worked.

Road Warrior
Something to consider about the height, it isn't just the height of the van when on level ground and your garage opening height, because:

Most approaches to carports and garages are sloped, and if reversing a caravan up the slope, the height at the rear of the van will be considerably higher than the nominal van height measurement.

It will then be, bum up in air, particularly when the van weight transfers some of it's weight to the vehicle which then sinks a little lower than normal and accentuates the height of the rear edge.
Depending on the length of the van and the sink of the vehicle suspension there may be 150mm or even more height as the rear upper edge tries to go under the carport/garage opening.

Only as the axle goes directly under the opening is the caravan height correct and it is that measurement which many use as the reference measurement only to find out what they though was enough clearance is not enough at all.

You need to check the attitudinal change when looking at any van.
Cheers
Ross M