Amsteel Halyard advice

[Brion Toss]

Hi,
Sorry to have been so long in replying. You have a number of options for dealing with this halyard. It might be possible to thread it inside a cored 3/8" line, but aside from the difficulty you'd likely have a too-stiff rope. Another option is to use covered HM with a 3/16" core, and pull that into just the cover of 3/8" double-braid. This should be easier, and acceptably fat. You could even strip the HM cover off much of the core rope, so that it was less bulky when the loads are low, early in the hoist, and big diameter isn't so important. And, further , you could leave some of the original core intact, saving on expensive core.
Inside Regatta works well for runners (that's how we do it), but you'll have to whip or serve the Regatta end down to the HM, and this juncture could be vulnerable to chafe. It'll be the same with any line too fat to bury into the HM. You'd also need to bury the HM a long ways, so that it is past the stopper and/or winch even when you are reefed. And even then you'll want to stitch generously, so the core doesn't want to slip as you hoist. As above, the HM needn't run the entire length of the cover.
Fair leads,
Brion Toss