I own 1911s from all the "big four" --- Baer, Brown, Nighthawk, and Wilson. It is wrong to call these "production" guns. Each Nighthawk, for example, is totally built by one gunsmith
From all these manufacturers, you can start with one of their models and ask to modify those. Some allow more leeway than others. But you can probably get what you want since you are looking at a fairly basic pistol. Now, some of them may not use certain parts made by someone else. I doubt Brown or Baer want to use the extended thumb safety from Wilson.
Last pistol I ordered from Nighthawk was a Falcon and I changed the front and rear sights, changed to slim grips, and changed to a medium length trigger. Before that, I ordered a Brown with a different front sight, had the barrel cut so it had a reverse crown and was flush fit, and added serrations to the rear of the slide.
I think that RickB hit the nail on the head with the word "bespoke" when it comes to custom 1911 pistols. Bespoke is defined as being made to order & custom made to fit a particular person or individual specification. It is the difference between and off the rack hand made suit and a suit build for you and you only from your measurements by a tailor based on your specs. There are smiths out there like Don Williams of the Action Works who will use the parts you want on your "custom" pistol. He will take your request, your individual desires and make it work. He has the knowledge to advice you and help you build spec a custom pistol and the talent to build it. That cannot be said of every "gunsmith".
For example on this BHP I wanted Harrison 1911 sights. Harrison does not make sights for BHPs. Don took standard 1911 sights and modified them to work on the BHP. He then tailored the front sight to match the point of aim point of impact for the BHP vs a 1911. I wanted a certain finish and he specd that out for me. He produced a custom thumb safety built from the factory safety. We talked about the Garthwaite flat trigger vs the C&S trigger. I chose the Garthwaite version but still used a C&S hammer and sear. What I ended up with is a one of a kind pistol. It is different then any other BHP on the planet. It is what I wanted nothing more nothing less. This is the pinnacle of bespoke because it is both made to order and custom made to fit a particular person and an individual specification. "Why Do You Think I am Paying You if Not to Have My Way?”
-Charles Portis True Gritt
Guns like 1911s from Les Baer, Nighthawk, Wilson Combat, Guncrafters etc... are close to this but are much more like a Ferrari. Les Baer 1911s can built to order so, all Ferrari sports cars are made to order, so in one sense they are bespoke. However your choices are limited to what is one the menu and based on the Ferrari or Les Baer foundation. You cannot ask Les Baer these days to build you a pistol based on a Wilson frame and slide using a Kart barrel. Just like you cannot ask Ferrari to use a Bugatti engine or put a Ferrari engine into a Buggati body. You however can pick your color. You leather, how much carbon fiber, which engine controls you want, etc... On a Les Baer you can add or remove front slide serrations, add a 1.5" guarantee, get stainless steel, change the sights etc... but all your choices are within the Les Baer universe.
It will still be built to order but it is not a whatever you want custom. When you buy the Ferrari or a Les Baer you are buying into a certain amount of restrictions because you like Ferrari's or Les Baer's take on a sports car or a 1911 pistol respectively. If you want a 458 Italia you can only customize or personalize it within the Ferrari universe if that makes sense. I see the semi-custom 1911 builders to be similar. There are many good 1911 houses and you pick the one that closely matches your personal aesthetic, your intended purpose and your budget. From there you accept the limitations of that particular builder and pick a pistol.
I don't have the numbers but I believe that more people buy the standard configurations off the rack vs actually customizing a stock configuration which pushes these guns further out of the world of "bespoke" IMHO. This clouds the issue even further because some Les Baers of 100% off the shelf while some have limited customization. Dealers like CrazyJohn even "custom order" pistols which they stock in their inventory to allow people options without the wait often associated with custom orders. I have a Les Baer TRS and it was not built to order nor was it custom made to fit a particular person or individual specification. It is an off the rack handmade suit not a "bespoke" pistol again IMHO. It is still a high quality pistol and one of the best in the safe but it is not "bespoke".
Now Wilson does have a true custom shop which will work on approved frames, slides and barrels but all the new parts that they will install are Wilson parts except for some sights IIRC. Still a great way to go if you have bought into Wilsons approach but it is not pure "bespoke" because while it is built to order it is not truly custom made to individual specifications because they have greatly restricted your choice of parts.
There is more than one way to skin a cat. I personally believe that the 1911 house like Nighthawk, Les Baer, Wilson etc... make excellent pistols. They are some of the best gun on the planet without a doubt. They are better 100% better than having the local Bubba smith slap whatever parts you bought at Brownells into your stock Govt pistol. They are certainly heads and shoulders above even the best mass production pistols like Dan Wesson but they are somewhere in between mass production and true "bespoke" IMHO. I know that Seven and others will disagree but that's half the fun of these forums isn't it.