given that compact cores are an older technology relative to the standard core, and that the IS never lost the technology to manufacture new standard cores, i suspect that they just needed data on what settings to input into the manufacturing lines. given they lost a lot of data on the actual physics behind the KF drive, they wouldn't have been able to work that out from base principles. the Helm core filled that knowledge gap, and probably had some details on the setting themselves.
Transit drives though they didn't have any infrastructure for. while they can build stuff for dropships, those are far smaller than the drives needed for even the lightest warship. and dropship drives would include a lot of features not needed for a warship (like systems to allow use in atmosphere, water landings, etc.), the removal of which would involve a substantial redesign of the engines themselves. and let not forget that the drives also provide the electrical power for the ship, which a warship would likely need a lot more of by tonnage than a dropship would, given things like the better sensors, stronger maneuvering thrusters, and possible presence of extensive energy weaponry (capital class or otherwise)
none of those are insurmountable hurdles on their own obviously, since they would all be stuff they could work out using existing knowledge. but the issue is one of scale. none of their dropship drive factories would be set up to produce drives as large as a warship would require, and it wouldn't be quite as simple as producing a bunch of small drives and strapping them together in a hull.
so i can believe that the transit drives were the last hurdle.
Comstar had maintained and even built new warships during the succession wars, and thus Terran factories for warship transit drives still existed, so them manufacturing the drives made some sense too. though i suspect that prior to Tukayyid and the Schism, the factories were under orders to drag their heels on production, to slowdown the successor state's warship production, which would not have suited comstar's long term plans.