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Trying to rank a homepage for all your keywords is a fairly difficult task in any industry, and usually service, product, and blog pages are used to target certain keywords so that you aren't putting some much pressure on your homepage to rank. The fact that you have "tens of thousands" of links is a little concerning to me, but if you believe they are all legitimate then more power to you. I would try to increase the content quality and quantity of the homepage and if possible decrease the amount of anchor text links as Google may be seeing this as spammy.