Bleed axe crafting advice

Hello exiles I'm looking for some advice on crafting the axe for my eviscerate bleed character. This is the axe atm and I'd like to continue crafting on it:



I think it has a lot of potential with its 2 good prefixes (flat phys and bleed dot multi) and an open one for crafting %phys.

My goal is hitting the elder suffix "Hits with this Weapon have Culling Strike against Bleeding Enemies, (30-49)% increased Physical Damage" and ideally multimodding %phys prefix and phys dot multi suffix.

The best way to hit the elder suffix that I have found so far is:

multimod -> pref. cnbc -> block last prefix -> reforge phys

This should give me a 1 in 9 chance to hit (on an ilvl 84 base it would even be 1 in 8).
Some experimentation on craft of exile suggests that filling the suffixes is quite unlikely.
If I hit 2 bad suffixes I'll have to pref. cnbc -> scour or maybe cannot roll attack -> annul if it's attributes or resistances I want to remove.
If I hit my targeted suffix + another dead one I think I'll settle for now and just craft %phys, unless I can annul the bad mod with cannot roll attack.

This is quite an expensive craft for me (4 div per try, 2 more to clean up if I hit 2 bad suffixes) so I'd like to make sure this is the best way to do it and I'm not missing anything obvious. Does any of you guys have any advice or ideas on how to improve the process? Or maybe I should target different mods altogether?

Just in case: Buying a fractured base or something like that is out of scope for me. I'm in trade league but I'm playing self-imposed SSF. I cheated a little bit with basic currency in week one but all my gear is self found and I want to keep it that way :)

Thanks in advance!