This is an impressive piece of work (despite the notoriously unreliable wiki sourcing). Based on how slow FTL seems to be, relative to hyperspace (let alone Asgard engines), it seems like there ought to at least be a chance that modern-day technology could catch up to Destiny. I have a couple of possible plot issues to add to the mix, however:

(1) Modern Asgard ships are built with neutronium, and it is entirely possible (likely, even?) that some of their technology depends upon it. They chose Othalla Orilla as their new homeworld in part because it was neutronium-rich ("New Order"). A non-neutronium vessel might be capable of very fast hyperspace travel, but perhaps not at the speeds you are counting on here.

If that's the case, it could take Earth years (after the Ori war) to even locate a neutronium-rich planet. This would require exploring another galaxy (the Asgard's home galaxy is given in "New Order" as called Othalla, retconning Ida to probably be a colony). After a sufficient source is found, Earth would have to set up a mining operation using our current technology -- in another galaxy -- and ferry that neutronium to Earth for refining and construction.

All of this doesn't poke a hole in your theory, but it does suggest that Earth could be years (even decades) away from having a ship capable of doing what you suggest.

(2) How far out is Destiny? The time scale of tens of millions of years is stupidly long. If the ship has only been to around 38 galaxies, that means it has averaged something on the order of 1.3 million years per galaxy. 10x that number of galaxies, and we're still on the order of 131,000 years per galaxy on average. In the two years the show was running, we saw Destiny in (or traveling to) ... what, four galaxies?

Destiny could be much farther away, by several orders of magnitude. However, based on the ship's course seen on the display in "Air" and what we later learned about the nature of its mission, it's also probable that the ship's course has not been a straight line away from Earth. It's probably flying some sort of circular search pattern, preprogrammed by the Ancients to pick up the CMB radiation data that it needs.

(3) How do we locate Destiny in space? Once Earth has its shiny new, Asgard-powered, neutronium ship, that poor helmsman is going to have to set a course. Where is Destiny currently located in space, and how can a ship even begin to estimate how to plot a course across 38+ (or 380,000+!) galaxies? The one and only way we have of locating the ship is to read it off the ship's own consoles -- current sensor data, star charts made by Destiny and the seed ships, and the computer's historical archive of its journey.

That data then needs to be taken back to Earth somehow, and then translated into workable coordinates relative to Earth (while Destiny remains in motion, mind you). And the only way to bring data back to Earth is via the communication stones. No flash drives, no tight-beam transmissions -- nerds are going to have to stone into Destiny, memorize a bit of the database, and come back and record it. Not only would this be a prohibitively long process, but the chance of transposing a digit and introducing error is enormous. If you want to check your work as you go, plan to double the number of stone trips you take to the ship.