A low AMH doesn't mean you can't conceive naturally, it just means your egg reserve is lower so you have less eggs with which to achieve that. Assuming nothing else is wrong there is no reason to think you won't eventually conceive naturally, especially given you have before, it may just take longer. It's unlikely your AMH has fallen off a cliff in the last couple of years, it was likely low before as well, you just didn't know.
The reason people have IVF for low AMH is usually time related ie they are wanting a baby now and want treatment to try and speed things up (common misconception that it will, it may not) or they are older with lower chance of successful pregnancy anyway and less time to play with in terms of length of time it may take to conceive. I was in the former category - we had IVF for our daughter after two years failing to conceive naturally in my early 30s, and I was fed up and impatient. All other tests fine. AMH was 6. We conceived our daughter from our only embryo of our first round. Subsequent rounds for a sibling (3) had the same result of one embryo each, all transfers unsuccessful. We drew a line under treatment after this only for me to conceive naturally for the first time in 7 years this year, age 35. That sadly ended in miscarriage but I conceived naturally again immediately and this pregnancy is going well.
We had our treatment at Kings fertility and I would highly recommend them if you go down that route. The essential fertility guide by Robert Winston is a must read in my book before going into treatment, as is a good scan through his website the genesis research trust and the HFEA website. Both give you the current status of best evidenced practice in fertility treatment. Don't lose sight that private clinics are first and foremost money making enterprises for the most part. It's best to do your own research as to what is likely to help you (and what won't) alongside hearing recommendations from consultants.
Re egg quality - nothing has been robustly demonstrated to improve this. I personally wouldn't waste money on expensive supplements etc. Vitamin D and folic acid are sensible to take when TTC as most people are deficient in vit d and folic acid as recommended by the NHS. Otherwise a normal healthy lifestyle (not smoking, regular exercise, maintain weight within normal BMI) is fine with the usual occasional treats etc perfectly acceptable. Limiting alcohol and caffeine as per usual NHS guidance is again sensible but you don't need to eliminate completely unless you want to.
Wishing you luck going forwards.