I deliberately rigged my space probe example so the use of gravitational assists would not be feasible. Here in our solar system, we use planets to help speed up and slow down spacecraft, or to abruptly change direction. But the velocities are usually a few tens of km/sec.

In my Far Centaurus* probe, we enter the Alpha Centauri system at 30,000 km/sec. I don't think gravitational slingshotting is going to gain us all that much, we are already way past the escape velocity of all the stars and planets in that system. We are entering that system so fast that in order to change direction even slightly with our "secondary propulsion system" we'd have to start boosting months, or even years before entering the system. The probe will be in the cis-Centauri environment for only a few hours at most, and the local gravities would have little effect on it.

Your comments on interferometers are interesting, but its been a long time since I studied them, and that was when they were used in radio astronomy. Two separate telescopes were linked together, at first by a cable or microwave link. Later, atomic clocks were used to synchronize the two. But the problem of different parts of the interferometer being light-hours apart, with the distance known only imperfectly, may be insuperable.

Fortunately, parallax work is not the same as interferometry, there is no wave interference involved, the process is just pure geometry, in fact, no real physics is involved at all.

But astronomers have experience with much longer baselines than solar system-sized ones. In the technique known as a secular parallax, the base line used is not the diameter of earth's orbit around the sun, but of the sun's orbit around the galactic center. The sun orbits the galactic nucleus at much higher speeds than the earth orbits the sun, and you can wait months or years to give yourself a really long baseline.

Check this out, from the Wikipedia article on "Stellar Parallax":

The motion of the Sun through space provides a longer baseline that will increase the accuracy of parallax measurements, known as secular parallax. For stars in the Milky Way disk, this corresponds to a mean baseline of 4 AU per year, whereas for halo stars the baseline is 40 AU per year. After several decades, the baseline can be orders of magnitude greater than the Earth–Sun baseline used for traditional parallax. However, secular parallax introduces a higher level of uncertainty because the relative velocity of other stars is an additional unknown. When applied to samples of multiple stars, the uncertainty can be reduced; the precision is inversely proportional to the square root of the sample size.[15]

* A shout-out to A E van Vogt, author of the short story "Far Centaurus", about astronauts who use suspended animation on a sub-light spaceship to travel to Alpha Centauri. When they get there, after hundreds of years in transit, they find planets in the system long settled by Earth colonists. FTL travel was discovered after our protagonists left Earth, and by the time they got to their destination the Centaurus system had been thoroughly explored and occupied. They are treated as honored guests, but are totally out of place in the future. Their science/tech skills are obsolete, the customs of the future are alien and disturbing, and even the English language has changed so it is unintelligible to their ears. The colonists (who had been long expecting their arrival) had to educate linguists in antique English so our sub-luminal crew would have someone to talk to.