You're right, StarFleet didn't know exactly where the probe was, just a very rough patch of space, that's why Voyager had to go find out and perform a search grid to use figure out where the probe really ended up.With due respect, that doesn't make any sense and it contradicts what we saw on-screen.
Two things from the episode: (1) Starfleet loses contact ~2247; (2) by 2377 Voyager is already in the neighbourhood and follows the probe’s recorded trajectory, with Kim suggesting a small “skip ahead” for local anomalies.
If the big jumps happened after 2247 as you suggest, Starfleet wouldn’t know where to send Voyager and the recorded trajectory wouldn’t point anywhere useful. If the big jumps happened before 2247, you wouldn’t have 180 years of comms because as we know, such jumps mess with navigation, communications, and it would be impossible for SF to track the probe consistently that way.
That’s why the anomaly-carousel model contradicts the episode. The boring explanation - routine refuels → two era upgrades → final drone pack—puts the probe ~29.7 kly out before 2247 and matches the search pattern on screen.
It took over 5 days of searching and Harry Kim found the probe in Grid 310.
But the issue is we have no way of knowing how it relayed signals for 180 years because that detail was never divulged.
We know that during the NX-era, StarFleet dropped SubSpace Relays as they got further into the frontier.
For Friendship 1, we don't know how many small SubSpace Relays Friendship 1 was packing, especially with the modern availability of tiny Cube Sats & Nuclear Batteries to keep those sucker powerd for a very long time.
Let's do some simple napkin math. Let's say you need a SubSpace Relay Satellites every 100 light years to boost the SubSpace COMMs signals of that era.
30,000 ly / 100 ly = 300.
So Friendship 1 would need enough room to carry at least 300 of those SubSpace Relay Satellites
And we know that StarLink itself packs tons of little Satellites that are slightly larger than the Cube Sats that we talk about.
Imagine packing your Probe's Cargo Hold with SubSpace Relay Cube Sats to relay signals back to home, then that makes communication plausible, even with degradation of the SubSpace Radio Signal over time & distance.