Ok, I think there might just be an issue in the calculation somewhere.
Looks like you're using CBT-style values (which are just ASx10), but that's fine. Your base values, though, should be before heat. So you should be getting 40.6/4.06 for Short, 48.6/4.86 for Medium, & 32/3.2 for Long. It looks like the discrepancy is you didn't include the LRM damage values in your base damage. Also, base damage doesn't include heat modifications, that's the next step.
For the heat modification, the assumption with AS is that your movement heat is already accounted for, & you're only adjusting for weapon heat. Hence, the calculation per bracket is (Base Damage) x (Heat Dissipation) / (Max Heat - 4), assuming your max heat exceeds the dissipation for that bracket by at least 4 points. For Short & Medium, max weapon heat is 42 (exceeds by 12), so the calculation is (Bracket) x 30 / 38; for Long, max weapon heat is 32, so since it doesn't exceed it by 4 you don't worry about calculating overheat but you still double-check the heat-adjusted damage. More importantly, since 32 - 4 = 28, which is less than your 30 dissipation, Long range isn't heat-adjusted. So, there's no OVL ability, & your Long damage is 3.2, rounded up to 4 (which matches MUL). For Short, it's (4.06 x 30 / 38) = 3.205, rounded up to 4, which also matches MUL. For Medium, it's (4.86 x 30 / 38) = 3.837, rounded up to 4, again matching MUL. The original unadjusted-for-heat numbers were 4/5/4; since there's a difference in the Medium bracket, you have OV (Overheat) 1, which matches MUL. Your heat calculations were assuming 44 max heat (including the movement heat), which threw off your adjusted damage calculations.
As pointed out before, Artemis precludes the use of alternate ammo, so the LRM#/#/# ability isn't available. IF#, however, is available, & you were very close on its calculation; the base number is 1.2, but for IF# it's rounded "normally" (i.e. round down if it's under .5), hence the IF1 from MUL.
Still...you were very close in your calculations. Had you remembered to include the LRM damage for Short/Medium, & the ER Large Lasers for Long, your rounded attack values would have matched MUL (30.45/36.45/32, modified to 3.045/3.645/3.2, rounded to 4/4/4), & you only would have been off on the IF#.