keeping valuables safe

I use a silk money belt-type pouch that hangs on a sturdy ribbon around my neck, under my dresses. Very easy to fish it out if needed. That said, it sounds like your plan is a good alternative. Whatever gives you peace of mind without being inordinately fussy when you are on the go, is the thing to do.

I do exactly as you plan. I have been carrying the same Baggalini cross body anti-theft bag for at least a decade. I do feel like a sherpa sometimes with the lanyard for my phone and the bag but haven't come up with anything better as an all in one. I do put a little lock on a section of the crossbody where I keep things I don't need while out and about; (it's an old bag so not like one of the current Baggalini's with locking clips.)

I use the same old bag as mentioned above and just usr a diaper pin to hold the zipper in place and it works out very well.

The silk passport neck holders are very comfortable against the skin, and the straps are as thin as bra straps. This is my mode of choice, and I purchased mine from Eagle Creek. I am most comfortable with my passport against my body.
There are also stretchy waist passport holders available from Amazon.
Whatever you choose, have a great trip!

Where will you be traveling?

I never carry my passport unless I am traveling from place to place by train. Or flying.

Respectfully, I think you are overthinking just a bit.

Yes - passport copies in several places is a great plan! That said, for the rest of it…

I carry my purse. It happens to be a nice leather crossbody bag with a zipper, but I didn’t buy it to be a fortress. It’s a cute, sturdy, high quality leather bag. The long strap detaches, and I have been known to leave the strap behind and carry the bag by the short handles. :-)

I put my phone in my bag when I am not using it. No lanyard. Sometimes I have my phone out when I’m at a restaurant or on public transportation - or just when I am sneaking in a quick game while idling somewhere.

Similarly, I do not use a money belt. I have my cards loaded on my phone for contactless purchases. I have physical cards in my wallet, which I carry in my purse.

There are pickpockets in Europe. You cannot entirely eliminate risk. But carrying money belts and overly fussy wallet/bag/contraptions is, IMHO, over the top. Just pay attention - practice situational awareness - and know what to do if you lose anything (how to call to turn off cards, etc.) You know - just like you would do if you were home in the states and got ripped off.

I think your plan is good. In Italy the law requires everyone to have an official ID, so it’s good to have your passport on you just in case.

I’ll just add a general comment and that is that a money belt is “deep storage” and you would not be getting into it during the day so it might work under your dress. It might be hotter than you want though.

I use a Stashbandz moneybelt. It has 4 pockets spread around the belt which eliminates the unsightly bulk. If your dresses are form fitting, it may show but looser fitting should hide it.
https://www.stashbandz.com/pages/travel-money-belt

I wear dresses in hot weather in Italy, and still have a moneybelt underneath with my extra bank cards and passport.
Mine is cotton and I put the contents in a ziploc bag, then wrap paper towel around the bag to be less sweaty.
It’s got an elastic waistband and no clips or fasteners so less likely to fall or come undone, unless you tuck it into your undies!
As Pam said, you’re not going to be needing to get into it as it’s “deep” storage.
If you do, then go into a washroom or changing room in a shop to do so.
A neck wallet is also a good idea.

Volva is 100% spot on- and situational awareness is a key part of keeping things safe.

I am male and never worn a dress, so I can't comment on that issue.

I used to wear a money belt, but changed to a neck wallet. I position the neck wallet under my right arm. I can access the wallet by unbuttoning my shirt a couple of buttons.

My wife has a pack safe purse and holds it under her arm.
Italy is a concern for pickpockets, especially in large cities. However, Barcelona is the pickpocket capital of Europe.

Your plan is fine. Be aware of your surroundings and know the common distraction techniques; particularly in busy choke points and tourist areas. Common sense things like Don't keep your phone on the table at a sidewalk cafe.

Yes you need to be aware of the people around you, what you are doing and how you carry your purse. I've never had an "anti-theft" purse. I have a small flat LeSportsac bag that is enough for my phone, a small wallet, tissues and my passport. I wear the bag cross body with the strap very short so it is more or sitting under my armpit. and as I usually travel in the fall - it is small enough to wear under my outerwear jacket. I don't like lanyards because the weight of the item hanging from it and the swaying annoy me. My phone is either in my purse, in my hand or in the zippered pocket of my jacket.

When I'm sitting in a restaurant/cafe, I keep the purse on my body and may lengthen the strap so it's long enough to sit on my lap. I never sling my purse on the back of a chair.

If I need to access something out of the purse I do it where I'm not in a packed area and I have space to dig around in it.
To my mind the anti theft purses are excessive. I keep a paper photocopy of my passport in my luggage and have a photo of the important pages on my phone as back up.

I have a much larger purse that I use for the days when I'm travelling between cities - it's large enough to hold a book and/or water bottle.

Seashell, the OP: Where are you living??
You'd know, Italy is not a country full of criminals. Of course, pickpocketing happens, as all around the world. And it happens more often when crowds are there. But let me say: we are travelling to Italy every year a few times, every time 2 or 3 weeks driving around with our own car with german plates. We always have our luggage in the car, inviible in the trunk (it is not possibly otherwise. And we never wear a money belt or anything else. If you wear a belly bag you would cry out: I am a tourist waiting for beeing robbed.
Put your money and your creditcard in any pocket near your body, not in the rear pocket of your jeans. Be aware of your sourroundings and everywhere on the world.
BTW: It is the law in Italy: every non-European tourist have to have their passport with them everytime. A copie would not do it, because there is no immigration date on it. If you happen to come to a police controll it could be a very bad experience to you.