Interferometry relies on measuring the interference pattern between two points simultaneously measuring incoming radio waves. Each element of a baseline must be measured at the same time.

If we were to allow the Earth to rotate around the Sun and measure components of the same baseline at different times, we would violate this.

One telescope each at the L4 and L5 Earth-Sun Lagrange points, coordinating their activities?

what about space telescopes in orbit at earth's radius at various points in the orbit?

The concept has been done, though not with such a large baseline: https://en.wikipedia.org/wiki/Spektr-R

I don't know what exactly the tradoffs are, but I suspect this approach has a lower sensitivity due to size of the dishes, it's more difficult to get enough telescopes to form a good image, and transmitting the data back is likely to be a challenge (the black hole observations were shipped on hard drives instead of transmitted via the internet. Even achieving a broadband-speed transmission rate with a deep space object is difficult)