Welcome! It's quite possible your hair thinning is partly or wholly down to the seborrhoeic dermatitis and/ or underlying systemic inflammation. If that is the case Rogain would be attempting to treat the symptoms not the cause. Sulphate surfactants have been implicated in hair loss in susceptible individuals, the issue is believed to be follicular irritation/ inflammation.
You absolutely can treat SD within a CG or modified CG routine. SD is about your body's inappropriate immune response to the malassezia yeast's waste products, not the yeast itself which actually lives harmlessly on all of us. That inappropriate response may be partly genetic, partly down to diet and lifestyle choices, partly down to what products you are using.
Historically modern medicine/ pharmacy have tended to treat SD by trying to wipe out the malassezia with anti-fungals and remove the food source (sebum) with harsh surfactants. Research in the last decade has progressed rapidly, we now know that harsh surfactants like SLS are capable of thinning the skin barrier - this barrier keeps water in, bacteria and irritating substances out. The body can respond to these harsh surfactants by pumping out more sebum to protect itself, the last thing you want in SD!
Instead consider modifying your diet and lifestyle to be as anti inflammatory and nutrient dense as possible, a healthy body needs a balance of ALL the essential nutrients it does not simply need biotin. In fact you can do more harm than good in creating imbalances with a random supplement regime. Especially look at your intake of oily fish, sugar and white refined carbs. This is critical for reducing systemic inflammation, calming inappropriate immune response, strengthening the skin barrier, altering the amount and composition of your sebum, significantly affect hormone balance in peri- and post-menopause.
Secondly modify your skincare (scalpcare/ haircare) routine to respect and repair the skin's barrier function. This means avoiding all sulphate surfactants, traditional soaps and other alkaline products like baking soda. Wash your hair regularly but without excessive massage with a gentle shampoo at pH 4.5 to 5.5, this will respect skin and hair both of which thrive in fairly acidic conditions. Sulphate surfactants are proven to thin and dehydrate even healthy skin at concentrations as low as 1%, personally I found just shampoo bubbles
running down my arm was the main trigger for my elbow patch of atopic eczema - the week I quit was the week it cleared. My mother's SD reduced by over 50% simply by switching to a sulphate free shampoo and face wash.
Avoid or limit anything that is a known irritant or allergen: random plant extracts, fragrances, certain preservatives. Do look for ingredients like aloe vera inner leaf gel that are proven to be healing and anti inflammatory. Possible shampoos include Komaza Care Moja (pH 4.5, ceramides, allantoin, aloe) or Regenepure (ketoconazole, zinc, aloe, designed for hair loss!). I also like the Komaza Care conditioners and scalp care products, many are pH 4.5 and packed with proven skin and hair friendly ingredients.
Thirdly avoid all oils and butters rich in oleic acid, stearic acid and palmitic acid, that includes but not limited to olive, avocado, sweet almond, palm fruit oil and shea butter. Studies have implicated oleic acid as being the component of sebum and the waste product of malassezia that is the prime irritant. Stearic and palmitic acids are components of sebum that feed malassezia. You can patch test with coconut oil if you wish.
Do not scratch and limit heat as this increases irritation, inflammation and histamine release. Wash your hair in cool water, no steaming, towel turbans or hot hairdryers. If your scalp is itchy use cold compresses. Whatever products you use in future at home or in the hair salon always run patch tests on a delicate area of skin, ideally on your scalp.
The bad news: permanent dying is a disaster for the skin's barrier function, it is highly alkaline so may saponify (turn to soap!) the fatty acids in the skin itself and destroy the acid mantle. The acid mantle cannot be restored by 'resetting' the scalp's pH with, say, vinegar rinses because includes the beneficial skin flora that help keep malassezia in check. If possible forget dying for a while, if not switch to a semi permanent colour - NOT demi which still contains peroxide - and try to keep it off the scalp. If you return to permanent colour when your scalp has calmed and healed avoid ones containing sulphate surfactants (many of them), see if you can find a hairdresser using an acid based system.
Sorry for the essay but HTH.