Ferrite cores have terrible lead-times, much worse than semiconductors.
It's the core-gap that makes the part even harder to find in stock. Definitely find a second-source core, the bobbin can be a standard size and easier to procure.
But will it always be in stock? I say dream on unless you volumes are high enough.
For a standby-SMPS I would not make a transformer- it's cheap but don't forget regulatory approvals apply with the safety aspect.
Your manufacturing know how to wind/insulate/varnish appropriately or expect surprises.
I pick the SMPS IC and order an off-the-shelf transformer, from
Coilcraft,
Wurth etc. Epcos/TDK offer this.
If I need oddball windings, I get them to do it.
If I have no room, I change/make the enclosure bigger because this is already silly to have one component in the world suitable for a product. Unless you can afford to stock them yourselves.