I think this approach is fine. I must say having been doing this for years, treating hundreds and thousands of men I have been underwhelmed with the results with topicals. Injections can cause peaks and valley and I have many younger men inject twice a week that smooths out the peaks and valleys. I think it is appropriate to follow the advice of your primary doctor and endocrinologist. I have just seen too many men spend months or years with gels with sub optimal results. Many men are diagnosed with depression and are not really depressed (I have no idea if this applies to you), but the presumed depression is base dupon low T.
My recommendation would be to pursue this but if a few months pass and results are modest consider another approach. Pellets are one approach to have smooth levels of T and are placed every 4 months.
Are bioidentical hormones natural or not? The answer depends on your outlook. They are manufactured, so if that makes them less than natural in your book they will not fit into the natural supplements for testosterone replacement category for you. However, unlike synthetic hormones, bioidentical hormones have the same molecular structure as hormones created by your body. They can be metabolized and side effects are minimal. Bioidentical hormones are found in topical creams designed to help balance your hormone levels. These creams include products like:
Dihydrotestosterone (DHT) (referred to as androstanolone or stanolone when used medically) can also be used in place of testosterone as an androgen. The availability of DHT is limited; it is not available in the United States or Canada, for instance, but it is available in certain European countries, including the United Kingdom , France , Spain , Belgium , Italy , and Luxembourg .  DHT is available in formulations including topical gel, buccal or sublingual tablets, and as esters in oil for intramuscular injection.  Relative to testosterone, and similarly to many synthetic AAS, DHT has the potential advantages of not being locally potentiated in so-called androgenic tissues that express 5α-reductase (as DHT is already 5α-reduced) and of not being aromatized into an estrogen (it is not a substrate for aromatase).