While I agree with most of the OP.
This part, I don’t exactly agree with. The core and design of Mercy is the fact that she’s a pacifist. So giving her even more opportunity to go battle Mercy is not something I’m on board with… That, and the fact that seeing her with a pistol in one hand and a staff in the other, despite the fact that she normally shoots two-handed, would look pretty awkward in-game, IMO. The issue with Mercy has never been “she doesn’t do enough damage” with regards to how she’s played, as the “pure healer”. The problem I see, is that as a supposed main healer, she isn’t that engaging, rewarding, or impactful to play since the rework. She lacks a “big hero moment” that she had when she had mass rez, and with that now gone, as well as multi rezzes, Valkyrie has become extremely safe / boring to play.
Also, removing resurrect would be a huge mistake I think. Not only is it one of the most iconic abilities in the game, but it’s also in a lot of her artwork, highlight intros, voice-lines, etc. and is a huge part of what makes her unique and recognizable. If that’s removed completely, I believe that it would be a lot of work to try and “rebrand” Mercy as someone else, as they replace those elements of her kit with something else. Even the devs are reluctant to remove the ability completely since they know how memorable it is / how many people love it in the game. So removing that aspect with just her duel-weilding, is probably not the best choice.
I believe we are kind of losing the point of what Mercy is supposed to be, a pure healer and pacifist, with a high risk high reward play-style. I think that swapping both Valkyrie and Rez, would allow her to have both more utility than she has now, while at the same time, give her back the opportunity to make huge plays.
A rework I’ve suggested for something like this, among other fixes such as balancing Mass Rez to have more counterplay, and balancing Valk as an E move, can be found here if you’re interested, and it kind of takes the idea of Mercy’s core elements, and expands upon them to cater to both Valkyrie lovers and Ressurect lovers, rather than favoring one over the other. Meeting a sort of middle ground if you will, as well as other suggestions as well, such as adding a sort of burst heal mechanic, and earning rez charges rather than getting them for free every 30 seconds.
But in an effort not to throw away your original suggestion completely, Un-discussed is also her reload button while using her staff. That’s still a free button to use, and perhaps it can even be a toggle to your previous idea of duel-wielding as well. Where hitting middle mouse btn = Mercy swaps from single wield mode to duel wield mode, being less accurate as she shoots from the hip (and perhaps is locked into whatever beam she was in previously, meaning that she has to go single wield in order to switch), but on the plus side, has the ability to heal and damage at the same time, and also raising her skill floor a bit.
In all, I think that the other points made about Mercy are great ones, and I do agree. Mercy lacks utility right now, and many agree that she can use an improvement in the “exciting” factor. I also think that keeping rez, valkyrie, and expanding on them both is possible. And is perhaps a great way to change the hero just enough without having to start from scratch on her design.
But those are just my thoughts, other than that, good post. 
~Sincerely Yours xoxo,
a Lover of True, Fair, and Fun Balance.
xavvypls 