Does the ‘Fiery Soul Trap’ enchantment’s Soul Trap effect work properly on certain enchant-able weapons with unique properties

I have tried enchanting both a Silver Greatsword (described in-game as "Especially effective against the Undead") and The Longhammer (described in-game as "Rahd's hammer, the reduced weight allows it to be swung more quickly") with the Fiery Soul Trap enchantment (TES Wikia link) (which is also a unique enchantment in itself, in that it contains two effects in one enchantment: 10 pts. Fire Damage, and Soul Trap), but in my many attempts to use both, they aren't able to absorb any souls .

I checked if I have spare empty Soul Gems of the appropriate size, and I do. I always try to deal the killing blow, but I don't get the captured soul animation nor do I notice my Soul Gems filling up. When I enchant, I use a Black Soul Gem with a Grand Soul inside, and set the Soul Trap effect to '2 seconds'. The Fire Damage effect of Fiery Soul Trap is fixed at 10 pts. The enchanted item gives that purple glow (meaning that it has been enchanted) and its Fire Damage enchantment seems to work fine (enemies are lit on fire).

Note that both weapons already have unique effects but can still be enchanted.

Other details:

• My character which experienced this issue is a Breton.
• My character does not have the 'Extra Effect' enchanting perk (can put two enchantments on the same item). (In a normal weapon with no unique properties, you don't need the 'Extra Effect' perk to enchant with Fiery Soul Trap (both Fire Damage and Soul Trap will still work fine).)
• I'm using the mods: Unofficial Skyrim Patch, Weapons and Armor Fixes and Smithing Perks Overhaul. My full mod list here.

Is this because the Fiery Soul Trap enchantment's Soul Trap effect won't work properly on enchant-able items that already have unique effects?
If yes, is there a workaround for this (other methods, console commands or mods) that can force 'Fiery Soul Trap' to work on these weapons?