Salutations!
I just read through your comic to get an idea of the "Pillow Shading" that you talk about here. First off, I want to say that you have a cartoony light-hearted style that, funny enough, is perfect for playing with different kinds of shading. It's also an enjoyable style that works well with the comedic tone you've established so, those two things play off each other well. The "Pillow Shading" that you've been doing isn't terrible and it does give your work a little depth, but with your backgrounds being mostly gray barring the occasional full-background scenes, the shading doesn't do what shading is meant to: give your character's a sort of pop and your atmosphere emotion (that is to say, evoking emotion in a reader).
That being said, it doesn't make your work bad or something like that, it just means that with a few fun additions, you can take what really works about your comic up a notch and sure up any places you feel you need to. The best part about all of this, is that it happens on your time-frame. You can take your time, experiment with different things and see what you like. I've got a tutorial here that not only shows the basics, but has several posts and links on the matter at the bottom to help you find more resources while providing a basic run-down of shading principals. There's also this video here that can show the value (no pun intended!) in shading with regards to making the art pop:
I'd recommend learning more about shading and lighting just to enhance your repertoire of skills and then use them as you see fit. Your comic could really benefit atmospherically from shading. It could also really benefit from more varied backgrounds so the shading has a bit of an establishing scene, and your audience knows where it's coming from. When I read your comic through, every time you had a background to show off, it was lovely. They're bright, interesting, and I think sharing more of that would really help build the atmosphere of the work and put your clever ideas out there more visually as well.
Your premise sounds like a lot of fun to play with so, just remember to have fun with it yourself!
Try things and see how you feel about them. Hah trust me I know EXACTLY how painstaking lighting can become. Every time I learn new tricks and realize how much longer it's going to take me to do a weekly update, I get a little nervous. But I try it out and sometimes it works really well! (I'm stuck in a never-ending night scene right now so, I can't wait to transition into day haha! I actually DO keep a sun/moon calendar for my comic so I know what time it is at all times and adjust shading/lighting accordingly. I don't think you're going to have to get THAT in-depth with it lol but, I just wanna let you know, I understand the sheer amount of work it can become haha) At the end of the day it's all up to you how you want to do anything so, while I've offered advice and some resources here, you're not obligated to take it haha! Just know that, if you're ever looking for resources you can find tutorials on youtube, online in general, for just about anything! I hope I was helpful and I wish you luck with your work! Your comic is really fun and up-beat and I hope you enjoy the adventure as well!
Cheers!