Mountain bike tyre at road bike pressure
2.00 or 2.20 or 2.30 inch tyre that I would use at 7-8 bars (100-120 PSI)

Does such a tire exist?
No.
A little math...
The surface area of a torus is 4 x pi^2 x R  x r, where R is the large radius of the wheel and r is the radius of the tire here.
Let's put a 2.00 tire on a 29er rim...
4 x pi^2
  x 15&quot; (approx radius of wheel at center of tire cross section)
  x  1&quot; (radius of tire's surface)

= 592 in^2

Assume the tire surface area is only about 2/3 of that, or about 400 square inches.  (It's probably more...)
Pump that tire up to 100 psi and each of those 400 square inches of tire surface has 100 pounds of pressure pushing on it.
That's a total of 40,000 pounds of force trying to push that tire off the rim.
Even if the tire can hold, the bead of the tire will be pushing HARD against the rim, trying to tear it apart.
40,000 pounds of force for a 2.00 tire at 100 psi.  Pump a 2.40 up to 120 PSI and it's more like 50,000 pounds of force.
There's a reason why tires have maximum pressure ratings, and larger tires have lower maximum rated pressures, and it's not because higher pressure starts to increase rolling resistance.
It's because high pressures in a large tire are downright dangerous.