Since its release I have been mainly playing the Heavy Splatling. I think as others have said, that this is a great weapon since it excels at defense, but also pushing the enemy back, which is offensive for your team. I use run speed up, since it affects your strafe speed, which is fast you move with a charge, and firing, so it is very useful, with x2 of them you move about 10-20% faster, which helps to beat the faster weapons.
It is always better to retreat a little ways to attack again, and I turn into a squid to escape if I fear being surrounded, since I can then splat multiple enemies who are confused. The splash wall is extremely useful in all gamemodes, allowing you to choose more options, including mind games. The inkstrike is good, it controls space, and I use it to cover my own space if I am being attacked with no teammates.
I thought it would have ink coverage issues, but you just have to find favorable lines of fire to maximize your ink. I am usually #1 in Turf Wars, getting 800-1100 points without win bonus. It does have a high learning curve of charge time to kill close enemies, but it is fairly natural to learn. I might create a general guide to it, similar to my Octobrush guide, since I think both have a specific role in the team. Regardless of game mode, the Heavy Splatling must always be a splat and teamwork focused weapon, splat your enemy then move up, or stay and defend the choke point, spray walls for team mates, defend their superjump, that kind of thing.
I think I am going to try to get to ~500k points from Turf War, then take it into ranked. I am planning on maining it, since I feel that I can play any game mode with it and do well, with Splat Zones being the worst, since its shots don't count for much when taking the zone.
Also the victory animation is great, the "We did it!" hug with the Splatling is so funny and cute.