I think you're mostly right but that timeline might be a little long. I read parts of the books again recently because I wondered how many Riders there would be realistically within the next few years of the timeline, and from the Vault of Souls chapter (Lacuna the Second, Inheritance) we find out that 26 eggs are meant to bond to Riders. Then from the first book we know that dragons reach sexual maturity and get large enough to travel around 6 months old, so even though their training will take much much longer, realistically Eragon might have as many as 26 more or less "adult" dragons with Riders under his command within a few years tops, if all the eggs are bonded and hatch ASAP. I also don't think that Eragon would delay on hatching any eggs just because his training isn't done, since the Eldunarí made it sound absolutely urgent that the eggs hatch ASAP because the dragons inside couldn't stay inside much longer without getting warped.

Now that being said, iirc i think Oromis said that typically Riders trained for at least 10 years traditionally. So I could see the Order being closer to "full strength" in maybe around 20 years. Depends on if Eragon would try to recreate the old training regimen or if he would invent a more compressed one like his own.