the functionality I need is similar to that of GeoCompressor from Hexagon, with the difference that I need to create GeoPackages instead of ECW.
It might be that you are not so much running into the limitations of GDAL as you are running into the differences between ECW and GPKG.
ECW is a very different technology than GPKG. Part of the objective of ECW is allowing extraction of subsets of imagery (zoomed in views, zoomed out views) for viewing in a very fast way, albeit at the cost of (usually) lossy compression and slow performance for writing/analytics. GPKG, in contrast, is more of a general purpose DBMS format, albeit a slower database than, say, PostgreSQL.
Saving to GPKG, therefore, will not get you the same functionality you get with ECW. It will be different functionality, with a different balance of advantages and disadvantages.
The only format I know that combines the benefits of both, fast access and viewing with larger data, plus fast DBMS for general purpose, parallel, analytics and writing, is Manifold's native .map project format. Save the data to .map with Release 9 and then anyone can use the free Viewer to view it.
Can Manifold very rapidly merge several hundred gigabytes of different images into a single, seamless image? Sure. Can Manifold save that into GPKG? Sure. But Manifold cannot give GPKG the multi-resolution/wavelet tricks of ECW, nor can Manifold change GPKG from being a slower database technology into a faster one like PostgreSQL, or even faster, for GIS purposes, like Manifold .map.
Manifold, by the way, can also save to ECW for free up to the limits of the free ECW code built into Manifold. If you have a Hexagon license, Manifold can save to unlimited size ECW.