This is something I constantly struggle with. I have a hard time breaking this mindset that my conlangs look like English if they do even one thing in the same way that English does. The reason I keep getting into this mindset, is if I do try to avoid this I end up making what looks like a cipher of English.
Honestly, its rather hard to avoid. Certain features of a language automatically force others upon it. Many people have noted the striking similarities between configurational languages, which is often pointed to as proof that certain grammatical features will automatically force others upon the language. And even David Peterson, an obviously experienced conlanger who actually has a master's degree in linguistics says that coming up with the rules of your language isn't that hard as long you have an idea of what you want the language to be. After you make a few decisions, everything else will suggest itself. In one of his videos he points out how one early conlang of his turned into a disaster partially because he didn't choose a goal and stick with it (one thing he highlighted was what type of conlang it was supposed to be constantly changed throughout the process, I believe it started off as an auxlang but latee turned into an artlang, which it wasn't suited for because of its auxlang characteristics, and then into a personal language that was full of features he didn't personally like).
Anyway, what I'm saying is if I put one thing in my conlang that English does, it forces me to put in features that English also has because of that one grammatical feature. And of course force more things upon you, and its not long before I end up re-creating English grammar. You really don't have as much wiggle room as you may think when looking through something like the LCK and reading up on the list of all the things you can put in a language.
One thing I'd really like to have in my conlang is a relative tense system. Essentially verbs, can be marked for two types of tense: absolute (past, present, and future), and 'relative tense', which mark when something occurred relative to another point in time. I really like that system because its handy in storytelling, which is why I so want to include it, but of course that makes my conlang look like its using the English tense system, albeit a regularized version. Worse yet is of course aspect. If I add it in, then it really does look like the English tense system; English literally has a grammatical structure that perfectly replicates every possible combination in my conlang. And if I don't include it, well then I find it mildly annoying. Though I think that might just be because of bias towards my natural language, but why would it be? I'm an intermediate in German and it doesn't have aspect (well, its not supposed to anyway). German doesn't even have relative tense (at least, like English does). All it has is past, present, future, and pluperfect. That's it. Come to think of it, I never even learned anyway to differentiate a habitual action from a continuous one.
I just find this so annoying. I can't seem to find a sweet spot where a conlang doesn't look like I'm making a cipher of my own native language, and isn't entirely made up of bizarre exotic features that makes it completely impractical.