Well, the one thing I know that a Heavy Splatling does best is hold a point. Mostly, I would focus on overall Ink Efficiency and Defense. Here's some strong abilities more specifically:
Ink Saver Main: Allows you to use the Splatling for longer; most useful when the enemy is constantly pressuring you
Ink Saver Sub: Can use Splash Walls more often. My
personal favorite since I feel that the Splash Wall plays a HUGE role in the Splatling's kit.
Defense Up: Really helps to survive more hits from all attacks. The only problem is that I only feel they are worth it ONLY IF you have THREE Defense Up Mains (or the equivalence of that) since that Third Defense raises so many max hits on weapons. (Also and immense help against Strength Up chargers.)
Cold-Blooded: Reducing the effects of all tracking devices by 75%, Cold-Blooded is definitely one of the more useful abilities, and the Heavy Splatling is no exception to it.
Ink Recovery Up: Good for regaining ink fast. It's an okay ability to have, but I personally prefer Ink Saver Main for when the enemy constantly pressures you. Ink Recovery will only help if you're at a perch that enemies can't easily attack.
Damage Up: Since each shot does exactly 28 damage (before damage falloff), the 4-HKO can be raised to a 5-HKO if the enemy has three Defense Up mains. So I wouldn't suggest using more than one main, if at all.
Finally, if I can get extremely lucky with rerolling gear, this is what I would constantly use for a Heavy Splatling
Primary:
2 Defense Up mains
Cold-Blooded
Secondary:
3 Ink Saver Mains
3 Ink Saver Subs
3 Defense Ups (Acts as a 3rd Defense Up)