It always helps to articulate what you do and don't like about your current settings, and where you're playing (venues? Garage jams? At home solo?)
Here's what I put on your other thread:
"Fat, juicy, compressed cleans and raw power distortion is the name of the tone game. I'd think a high gain Marshall model for the dirt parts (with an optional boost) and a Fender model with a compressor and boosted mids for the cleans."
Thicker pick will definitely help bring definition to your sound. Ska punk is all about definition. Reducing the bass will also help with this. Maybe turn down the distortion too - too much gain can make your sound fizzy and weird.
The Katana is a great amp. If you like it, I don't think you need to switch it for another 50 watt amp. But part of what the sound you like from the band is likely a bigger cabinet like a 4x12... I guess I'm trying to say, from this comment and the ones I made in your other thread, try to make your sound "based on someone's else sound" rather than trying to "sound exactly like a certain band". It's a waste of time and money to continuously exchange gear in search of a specific sound.
You may also benefit from a nice workhorse multi-effects pedal like a Boss, Digitech, Zoom, Line 6. Those can be found for under $200 and contain a world of different sounds. The Katana plus a multi effects pedal plus your Tele would be an incredibly versatile rig for not much money.