One big problem (besides getting out there - hehe) is that you are looking in one very particular direction and need to move big distances (at a distance of ~500 au from the sun) to look elsewhere. I guess you could wait until the planet you are aiming at does another orbit around its star and flies through your point of focus again.
PS Voyager launched in 1971 and is now at 158 au! These distances are truly vast. 1 light year is 63241 au.
This is the space project that most excites me and the one I most hope we solve in my lifetime. Much more interesting than Mars (not that you can't do both).
I don’t know anything specific about what the parent is proposing, but I imagine it is using the mass of the sun as a gravitational lens. Because of the solar radiation there isn’t really much sunlight (read:any) that is directly reflected to an observer peering on the edge of the sun.. light travels in straight lines.
Basically, the way scientists used a solar eclipse to confirm the theory of relativity and gravitational lensing of stars ‘behind’ the sun to in front of it. Or like the way certain objects were lensed in the massive JWST shot that came out a couple months ago.
Or are mindbogglingly slow.
If we can reach 90% of lightspeed we would have a good Lorentz number to travel the whole milkeyway in a few weeks. We would see a very different earth though when we come back.
To travel 87,400 light years at near light speed, in a subjective time of a month requires a dilation of 87400 years * 12 months / year = 1048800, with a speed of:
(1-(1/1048800)²) c = 0.9999999999990908 c
which is about 0.27 mm/s slower than the speed of light.
For perspective, Voyager 1 has been hurtling through space since 1977 and has travelled a measly .002324439 lightyears.
The Universe is mind bogglingly big.