The stump blocks from Better With Mods don't render as round logs even when added to the whitelist as "betterwithmods.common.blocks.BlockStump" unless "Default to vertical" is true.

Is there a custom "Wood Log Model" that I could add to get this working without every log being vertical?

You can set the option to true without worries. Not all logs will be vertical, only the ones that don't have an axis defined - like BWM stumps.

Logs that do have an axis (i.e. you can place them sideways, not just vertical) will still have their proper orientation.