First of all, congrats on #4! How exciting!
Now on to your question... My husband and I are struggling with a similar issue. Vasectomy or tubal. I have a life-threatening condition that only shows up when I'm pregnant so it would not be safe for us to have more children. I think I'm pretty sure I want a tubal for one reason: I want to completely remove the temptation to get baby fever and try again and think maybe the next pregnancy will be different. I want to limit my options in a really permanent way if that makes sense. (BTW, I also had a surprise ectopic a few years ago with the Paraguard IUD. I loved my IUD, and I got a new one, but I can TOTALLY understand your hesitation for getting another one.)
So with that in mind, I talked to my doctor about it. If I have to have a c/s, which is extremely unlikely since childbirth itself is actually really easy for me, I will sign consent to go ahead and get it done then. If not, she said, it's just too much to deal with one surgery on top of having a brand new baby, and I can definitely see that is the case.
With that in mind, I plan to wait a few months and then have the Essure procedure done. I believe it was 12 weeks post-partum, but I can't remember exactly when she said they do that. It's completely hormone-free (I can't do hormones at all for health reasons) and she said it's even more effective than a traditional tube tie. I also understand it to not require general anesthesia. It's a little less surgical in that they don't cut you open to do it.
So that's what I plan to do. What I would absolutely NOT do it right after giving birth. You'll have enough to deal with then!