Before I answer your main question, I'll quickly address a couple of things you mentioned that technically aren't accurate. The first is that STAB doesn't multiply the base power of the move as you suggest, at least not directly. STAB is part of a separate calculation that is later multiplied with the main calculation, where base power is considered. More detail and the exact formulas are available on Bulbapedia, though in practise this only makes a difference of one or two HP points, so it's fine to use for comparison as you have done. Just keep it in mind!
I'll also quickly make sure that you're talking about Giga Impact as opposed to Hyper Beam. Unless you're playing a Generation 3 game, Hyper Beam works according to Slaking's much worse Special Attack stat and will be weaker than a lot of different moves on Slaking's physical side. Giga Impact is the same move except physical, so I'll assume that's what you meant in this answer.
So to finally address your question: no, Giga Impact is not always Slaking's best move, but it does come very close. Excluding moves that hit for 4x or 0.5x damage, there are only two moves in Slaking's learnset that will ever hit for more damage than Giga Impact, both occasions involving a super effective attack of course. Those moves are Gunk Shot and Focus Punch, which have 120 and 150 base power respectively. If we use the rough comparison with the base power, Gunk Shot produces 240 base power on a super effective hit and Focus Punch 300. Nothing else in Slaking's physical movepool is above base 113 power, which is the amount required to beat Giga Impact after STAB.
According to some numbers from Pokemon Showdown's damage calculator, Gunk Shot will deal about 7% more damage than Giga Impact on average, depending on the precise stats involved in the calculation. Focus Punch will average about 34% more damage, so Giga Impact is a ways off the highest output possible, though of course you'll only be using Focus Punch in very select scenarios. Even Gunk Shot is not included on Slaking's standard set for competitive, so in practise neither of these moves matter very much, and Slaking's strongest attack on its standard competitive set will in fact be Giga Impact apart from when it does 4x or 0.5x damage.
Damage calculations used to get these figures:
252 Atk Slaking Giga Impact vs. 0 HP / 4 Def Rapidash: 382-450 (140.9 - 166%) -- guaranteed OHKO
252 Atk Slaking "113 base power physical Ground move" vs. 0 HP / 4 Def Rapidash: 384-452 (141.6 - 166.7%) -- guaranteed OHKO
0 Atk Slaking Giga Impact vs. 0 HP / 0 Def Glalie: 292-345 (97 - 114.6%) -- 81.3% chance to OHKO
0 Atk Slaking Focus Punch vs. 0 HP / 0 Def Glalie: 390-460 (129.5 - 152.8%) -- guaranteed OHKO
0 Atk Slaking Giga Impact vs. 4 HP / 0 Def Azumarill: 292-345 (85.3 - 100.8%) -- 6.3% chance to OHKO
0 Atk Slaking Gunk Shot vs. 4 HP / 0 Def Azumarill: 314-370 (91.8 - 108.1%) -- 50% chance to OHKO
You can see in the calculation with Azumarill that even the small bit of extra power Gunk Shot has matters quite a lot, with the chance of an OHKO reaching 50% as opposed to 6%.