I don't know much about UFE except that those "little balls" can migrate to other organs including the lungs and cause serious problems. They can also damage the ovaries since the uterus and ovaries share blood supply. This can lead to an early and/or severe type menopause. Damage to ovaries (or their removal) is associated with many increased health risks and earlier death. Radiologists not gynecologists do UFE. Gynecologists insert "T shaped" progestin device (Mirena IUD?) so money could be part of the motive. There are insertion and removal fees and I've heard that some insurance plans will pay for insertion but not removal. IUD's have their own set of risks so be sure you understand those before going that route. Endometrial ablation is another procedure heavily marketed and done by radiologists but with serious long-term problems.
How much are you bleeding? Have you tried various birth control pills to regulate the bleeding? What about the non-hormonal prescription medication Lysteda (tranexamic acid). It's often very effective at reducing bleeding so much so that paramedics keep it on hand. At least with medications you can stop taking them if you don't like the side effects or they aren't doing the job. But with procedures, you're stuck with the bad along with the good.
Best of luck in getting proper treatment.
I assume your fibroids are causing pain or discomfort? Are you by any chance close to menopause when they shrink and can just wait it out?
I don't know much about UFE. However, UFE is done by radiologists not gynecologists. So bottom line, that would be lost business for your gyn. Hysterectomy is very profitable and grossly overused so chances are many gyns will tell you to have a hysterectomy.
I had one 10 years ago at age 49 and regret it every day. It is the surgery that keeps on giving "problem after problem."
Best of luck in getting information and treatment that restores your health versus causing a whole new set of problems.