Thanks for the details Gary. Is the section of the ferrite rod rectangular mm 8x4 or round Radius 8 with to flatten sides?

I have found this https://www.aliexpress.com/item/Tangda-soft-ferrite-rectangle-plate-core-ni-zn-material-4-8-50mm-magnetic-bar-4-8/32844810654.html
Disregarding the fact that the material could be different, will it work adding one bar at each end of the stock ferrite?

They can be hold in position inserting everything inside a 8mm pvc tube and leaving out just the coil.