My daughter is pretty spirited too and it can be very trying. I also look at these calm babies who will sleep or just chill in a car seat and it seems so weird to me. All the moms in my playgroup have toddlers that are still happy to snuggle up in a carrier or sit with their mom and my daughter will not have any of that. I don't think you need to worry that by keeping her happy at 4 or 5 months, she will never learn to deal with life. I think with a young baby, you just have to do what works and gets you through the day. You can worry about that other stuff when she's a toddler and starts having fits about how many cookies she can have
Something I've learned in my (limited) experience with parenting stuff is that the trying stuff is temporary. It may seem like it goes on forever, but it won't. Your kid will eventually outgrow this stage. Right now, baby Iris is teething and having crazy amounts of tantrums and it's making me nuts. But I tell myself that this is just a phase and take it one day at a time.
When she used to scream in the car, the only thing that would work was this one lullaby. No other song, just that one. Now if she's flipping out and I put on Lady Gaga, she is instantly happy. So keep trying stuff and maybe you will find that one random thing she likes.
Since you mentioned CIO, I have to throw in my two cents. It seemed cruel and heartless to me when Iris was Ava's age too. But we did it when she was around 1 year old, and it was a lifesaver. This may be an unpopular opinion around here, but our lives are much better since we used CIO to solve sleep problems. I am a better mother because I'm well-rested, more emotionally stable and my marriage is stronger because we get time to ourselves every night (we were cosleeping before we did CIO). Different things work at different ages--I wouldn't do it with a baby as young as Ava but it really did work for us later.
Anyway, hang in there! It gets better, I promise.