Weapon: from +3 to blessed +4

hi guys,
i'm currently playing a sigel knight and some days ago i found what i thought was a great deal, +3 apo cutter health 170 holy only 180kk. considering clean item now is 200kk @ah, it looked great to me, expecially since as a dmg sponge i don't really need a greater source of damage, next step will be r99 after ethernal + jewels will be done, which will likely be in lineage 4 year 2065.

anyway, when i bought it i didn't consider, maybe wasn't even yet aware of, giant's scrolls, so now i find myself in a tricky spot, since i most likely will have to gamble to get +4. not only, i actually really, really fancy that blue "apo cutter" name, (read: blessed one), so that's another goal i'd like to reach.

now, let's play pretend and say i have all necessary adena needed to do the trick; i do not, but one day i might. of course what we are doing here is some maths to find out the most efficient way, meaning highest success rate / adena needed.

the most straightforward way i can think of is buy r2 blessing scroll and then add bewr (might as well throw some € to enhance success rate). we are now at around 160kk, and if i'm not lucky enough to get it +4, i can always go back to giant's scroll (quite easily obtained by mentor).

some suggest to sell the one i have (with a nice gain) and add that income to that estimated 160kk from above to secure one in ah. i think it may cost a little bit more, but that's for guaranteed result.

another quite safe way would be to buy a clean one (with sa though, if that even exists), go with giant's scroll and turn it blessed with said r2 scroll, and eventually go with +150 atri stone.

i wanted to put down this kind of brainstorming more to sum it up myself, but since i'd do anyway, i thought why not share with community and listen to their alwasy precious advices.

p.s.: "you don't need it" is not an answer to this thread, what i'm asking is "how to", not "whether to".