Getting to X rank is a pretty good realistic goal to have and I'll assume it's specifically quad X.
As for branching out I'll get to that later.
As for not knowing what your problems are. It leaves me rather stumped on what to say as I don't want to make assumptions on what your having difficulties with. The best thing would be to see some ranked gameplay. If you have any let me know so I can get a better idea on what advice to give.
Now your weapon choices are all fine (imo you can get X rank with any weapon, but that's besides the point.) Here's my two cents.
- Heavy Splatling Remix (SZ/TC) - A strong pick all around. Not much to say other than play it like a splatling and not a charger.
- Custom Jet Squelcher (TC/RM) - I not too sure it's the best for rainmaker. It's a bit slow for a game-mode about hauling the rainmaker as fast as possible to the podium. Unless you find yourself carrying the rainmaker most of the time. Tower Control's slower pace is fine for it though.
- Custom Dualie Squelchers (CB) - You could honestly just use this weapon for all modes. Easy, comfortable, and a solid kit. It being more mobile than other mid-range stuff is also good for Clams.
- Nautilus 47 - I know your just trying it out, but I think it's a great weapon to stick with if you can. Afaik it's got wider skill floor than most weapons and leans a bit on support from teammates. However it can tackle most modes well and has good range with it's time to kill. I know some might say that Nautilus 79 is better, I generally agree, but I think it depends on how good you are with inkjet. If inkjet is not to your tastes then you should just use 47.
In terms of other weapons to try. I have a few suggestions.
- Tentatek/Kensa Splattershot - The jack of all trades that fits quite nicely within ranked. They don't excel at anything but they are comfortable in even the most dire situations (and lord knows that ranked is full of those). Maybe not a "main worthy" weapon for some but should be a go-to pocket weapon for everyone.
- Neo Splash-o-Matic - Similar to the above but with more emphasis on painting/mobility. It is also 100% accurate which, for me at least, is a huge plus. A good Clam Blitz weapon.
So you might notice that these weapons are what some would call slayers (I don't like that term but whatever.) I did this because all the weapons you're currently using are supports/anchors. I think it's important to get out of your comfort zone with how you play and try out different approaches towards splatoon and get different perspectives. These weapons are also pretty independent and don't need worry too much about what your teammates are doing. You should still obviously pay attention to them during the game but not as keenly as supports or anchors would.
Hopefully you found some of this helpful. If you need me to elaborate on anything just ask.