Do you think a 4th revision rhinoplasty is worth it but this time with another doctor?

There are probably several things that can be done to make your nose look more natural. A reconstruction of the tip, hopefully minor, bringing the tip back closer to the face, probably a small-ish augmentation of the bridge, but not too much.But this would be a very complicated, difficult operation because of your history, and I don't think you should let your other surgeon do it.You need to select a surgeon, have morphs made, do an excellent evaluation of the surgeon to see whether he has the skill to help you.
Remember that rhinoplasty is an exquisitely difficult operation to get right, and you should only have surgery if you are able to make yourself very confident in your surgeon's skills. The changes that your nose needs require advanced techniques, and skill that most plastic surgeons don't possess with expertise. For most noses, it's much better to not have surgery than to have inexpertly-performed surgery. Read my essay on how to stay out of trouble while selecting a rhinoplasty surgeon. And for those who have had previous surgery, it also discusses how to tell whether your first surgeon should be performing your revision. And it also discusses how to take photos that are best for online evaluations.
Your nose is also a perfect example of why computer imaging is mandatory in rhinoplasty. You need to know exactly what the surgeon is planning to accomplish -- what features he thinks he can change, and by how much he thinks he can change them. I always email morphs to my online rhinoplasty consultations. When you see the surgeon's goals in the morphs, you'll know whether he has an eye for an attractive nose, and whether he shares your opinion of what constitutes an attractive nose. You'll also know whether the changes he proposes are large enough to be meaningful to you, and whether he understands your wishes enough to address all of your priorities. How would you ever get that figured out without the morphs?

Thank you for the photos and your questions. If you have had 3 procedures with one provider and are still not satisfied, it is absolutely time to get a second opinion. Based on your photos, it does appear that you have a low bridge and an overprojected tip with a hanging columella. In my opinion, you should meet with a few rhinoplasty experts to discuss options. Please plan to bring all photos and operative records from your prior work in order to get the most out of your consultations. Best of luck moving forward!

I agree that you have a marked slope on profile and pointed tip with a relatively short nose that looks very surgical.   A revision rhinoplasty with cartilage grafts to decrease slope and soften tip should give a nice result but would like require rib graft.   it would be important to carefully choose your surgeon and look at before and after pictures to get a a realistic idea of what you can expect.