I don't think de-emphasizing gods is a good idea, as they are extremely interesting and fun to play with, especially with god switching thrown in. I fully agree of course that any 3 gods should provide useful bonuses to every class on every level, preferably similar in power, and possibly requiring adaptation and changes in strategy. I am aware that this is incredibly hard to achieve, but you already were pretty close in the previous version (except for Dracul, who is now a lot better than before even if you don't use lifesteal related exploits). Sure, one specific god was always (and always will be) the best for a specific race/class/level/prep combination by some varying margin, but I could get excellent mileage out of any combination with most classes, and it was often not that obvious which god would be best. Each of the gods has different times in the game when the boons and drawbacks are most important and when it is easiest to get piety, which leads to very interesting dynamics. Designing the gods to have some use for all playstyles was a great step in the right direction. I think simply nerfing gods and focusing on items is the easy way out, powerful but balanced gods (and eliminating exploits) would provide far better gameplay.
Shifting the focus from gods to items just means you will have to balance those properly to make sure finding one or more specific items in a shop will not be vital to success, and items are far less interesting than gods IMO. Probably also a lot easier to balance, in part thanks to the locker system providing guaranteed access to a single shop item, and in part due to being less complex.
Besides, the core problem will never go away. DD is a random game, and luck can always compensate for an almost impossible challenge or lack of skill to some degree, or make a normally easy level very hard. For me enemy composition usually had a far bigger influence on game difficulty than what gods I got. I think randomness is great, just trying to get rid of the extremes would be good. In a long game like Crawl you will almost always be unlucky at some points and lucky at others (if you survive the unlucky parts). In a short game like DD the odds can really stack up for or against you. The preparations help a lot with cushioning these extreme strokes of good or bad luck, and good balancing and clever design can do the same for gods and items. I just think emphasizing the more interesting of those two would be better.