This is a great question!
Parallax and stellar positions
To measure an object's parallax assuming no proper motion, we can get by with as few as two images of a foreground (moving) star against a background of several "fixed" stars. We only need enough resolution to make out one star's diffraction (Airy) disk from the other stars with enough precision to resolve the movement due to parallax.
You can measure the center location of a "blob" with much more precision than the FWHM of the blob, as long as you have plenty of photons and you can get a good handle on systematic errors and pixel-size-related issues. As long as these are separate and individual stars, you don't need to resolve each star's disk to 1 mas to get a relative distance between them with precision of 1 mas.
The Gaia spacecraft is an example of a space telescope with a modest (rectangular) aperture of about 0.5 x 1.4 meters, yet it produces huge volumes of extremely precise parallax measurements.
Over the period of a half year, Gaia does move to "diametrically opposite ends of the earth's orbit" and it records images continuously. The idea is to get five to seven images of most of the sky in order to separate out the parallax from the proper motion from the systematic and random sources of noise.
However, these are images and contain no phase information. As I explained in this answer to Is Digital Adaptive Optics Possible? the techniques we use to produce and record optical images generally lose all phase information, what you are left with is only intensity, not complex amplitude.
Interferometry requires the interference of amplitudes and the phase of each signal is key. As pointed out in that answer, we can do this for microwaves and lower frequencies using high speed (GHz) ADCs and often some amount of down-conversion, but we don't generally do this for visible light.
For the EHT's image of the black hole, they used atomic clocks at each telescope's site and synchronized them using things like GPS time signals and nearby calibration objects in the sky.
Not that this hasn't been demonstrated for visible or near IR light, but it's not something you can easily put in a satellite. One way you could do this is share a laser beam between two spacecraft and mix it with a narrow range of optical frequencies from each of the telescope and record the resulting heterodyne signal with a GHz or hopefully much higher bandwidth. You'd also have to reconstruct the distance between the two satellites to the order of a wavelength of light to get any kind of meaningful data.
This is not impossible, but it is really hard and would be quite a technological and budgetary challenge.