you should learn to use pyfa, it tells you your effective DPS vs specific target.
THE FOLLOWING GRAPHS ARE WITH ALL 5 SKILLS WHICH YOU DONT. Especially you don’t have the sig amplifier skilll, nor the application skills for missiles.
here are the dips of a praxis with ONE RHML , no BCU, with the three missile types, and RLML with fury, against a triglavian frigate (245 m/s, 34m sig)
from here we can see that going rlml is worse than rhml with precisions. The max dips of the rhml is 49.1 DPS
going with application mods :
GC(precision scripted) vs painter :
2mods :
adding a rigor II :
with 2 rigor II :
with 1 rigor II and a grappler :
with 2 rigor II and a grappler :
so to deal maximum DPS(49.1DPS) you need two painters II, two rigor II, a grappler.
The RLML deals already max DPS with no application mod.
so now with 6 RLML and 3 BCU it goes 448 DPS which are applie dperfectly vs all targets. When the grappler is not applied, you will only deal 331 DPs though - so when target are above 10km, shoot the destroyer and the cruiser first. Then ask questions 
but now, since we know bot grappler and painter have an effect, what about using the other ammos again ?
actually with grappler active and close range, the CN deals more DPS
so the answer is : use RHML with CN, unless you want to save ammos price then use precision, and 2 rigor T2, two painters.
also I tested with polybolos and it does not increase the DPS over a standar BCU. (because the limiting factor is the sig)
Also the navy does not apply fully. Use a T1 additional rigor to get even closer to the max application(492 DPs over 504 max )
But then I think your tank starts to suffer a bit …
the fury outdps the precision with … 4 painters, 3 rigors, 1 grappler and one scripted computer (and still only reaches the navy )