Broad brush for a small wall.
You make the assumption that a woman wants a "girlfriend" or house keeper. Here's the thing, you make a good partner no matter how you are dressed or how you present. Great,you like to shop! It was an advantage in my marriage that I liked to shop, she didn't. So when she needed a new outfit, I would scout one out maybe buy it and see if she liked it. We neither one liked housekeeping. Lots of great male chefs in the world.
Do crossdressers make better partners? No. When you scan a few posts here you will see that many are self centered, difficult, spoiled, can I say liars? (at least not tellers of the total truth). They like having the perks of both genders but seldom take the dregs. Their tastes run in different directions. Some use it as a sexual fetish and when the act is done..it's back to being Mr A-hole again.
I can see where you think this should lead. Hey girls! Want a guy who is caring sweet kind wonderful, likes to cook and clean and will cuddle all night long while you bask in the lap of luxury? Date a CD! And if you act now we'll throw in ironing your panties FREE! Why? Because CD's love the texture and feel of your underwear and they get a great kick out of it! (restrictions apply, said panties must be lace and satin, very small and preferably a bright color.) It doesn't go there. You are who you are. It is a core concept most of us here try and explain. It should not matter what you wear. If this is an idea to get your SO to accept you, then you are barking up the wrong skirt. If they love you, as you, then your clothes don't really matter (at least between you two...you have to work through the in public and other places deal). If you, like most early CDs use it as a sexual toy, it won't work so good. If you just incorporate the ideals you stated in the OP, going shopping (if she likes that), cooking meals for you two, doing little things around the house (be they male stereotype or female), being there FOR her when she needs you, sharing anything you like to do and yet giving you both the space to be YOU, then those pink boyshorts under your slacks, or that little teddy you like so well, won't be a major issue. But you MUST communicate (two way street). If you let her see that you are really a good person who cares about her (and puppies and rainbows) then the CD thing will work out.
I was a terrible husband in my mind, I wear dresses (and she accepted that I was a TG), I cooked. But I still wasn't the great husband I could have been (see all the flaws listed above). Lucky for me, she knew perfection was impossible.