Thats a great question and one that in the same niche here in Ireland I ask myself every day.
Your list is one that I instinctively created and like you also immediately realised was the same as others. Here is what I try and do that I think makes the difference. It may sound cheezy and self-help book style but with my business now nearly 90% referral I feel that it has borne results. It may not suit you or your style so feel free to ignore.
Speed: There is a perception that a website design project should take x weeks. In some cases of course it can take weeks or even months. One of the areas that I am (overly) fanatical about all the time is automation and developing blocks of code / collateral that I can re-use again and again as foundation for client projects (websites in my case). This can be items like core style sheets, base themes / templates that can form the basis of operations. Making my WordPress (my go to CMS) setup super super fast through having a core set of plugins in place and the ability to set up WordPress in even less than the 5 minutes.
Then delivering early prototypes of website to customers who in my niche at least (SMEs) really can't distinguish good from amazing (more on that in a second. As a creative (lofty title) we tend to muse too much about the subtleties. I am not a designer more a developer so I haven't that anchor around my neck. I often argue with my designers 9in a positive manner) when they declare that a design isn't ready. Fit for purpose often will do.
Let me give you an example. We did a project last month with a client who had a horrible HTML website that even they knew was a dog from hell. I met with the client they wanted a "clean, simple CMS that had their logo and their existing content presented in a more pleasing fashion". So we created this for them http://www.grangewebdesign.org/eurosign/ - in 3 days. I won't share what we charged them for it but it is ready for deployment next week. Total man hours in and around 5-6.
The client knew this, we know this and they happily paid for it.
I know it isn't an award winning website - far from it - it is basic simple BUT fit for purpose. How we developed it so quickly was by applying a lot of good process and the items I mentioned above.
Yes we do better work and that leads me to the next point.
Best In Class Design
Your portfolio is king. The site above won't be in our portfolio. For obvious reasons. But every so often when you take a project that you know the site will get a lot of visitors you should pull out ALL the design stops to make it a work of art design wise. It may mean spending those extra dollars in time and eroding some of your own budget but I say do it. If (say) the end product is going to get 10K visitors a month (for instance) some of these may be potential customers and they may cone down your funnel through referral. Even if they don't you will have something great for your portfolio.
We do a mixed bag of wok in our company as it is the nature of the beast as we get clients with a wide range of budgets.
Last but not least you may already be this but this is something I finally decided to do early 2013.
This stems from my reading of a book by Stephen Pressfield. Essentially I now try and be super professional with clients. This is two parts. One is giving great service, proposals and deliverables and the other side is not doing work that isn't paid for. I used to be a sucker for this. "Can You do XYZ?? "No problem".
Now I quote it and price it properly. And guess what 99% of clients pay for it. My revenue is up as a result and I definitely feel my clients respect me more asa professional. There are hundreds of hours of unpaid work I have done which I now look back on with regret.
Your original question was "how can I differentiate myself from the countless competition?". I think this is the wrong question. I think your goal should be to make the next or current client a loyal salesman for you. AS they pay the last invoice you leave them as a delighted customer. Keep in touch with them. Touch base with them once a month with a phone call (not an email no no no). Use a CRM and keep record of their lives and their families and become a friend - after the project not during - during they are the client. Get a headset and develop a call list for them With the CRM you will have something to talk about.
Clients are your sales team. They will be at a meeting or bar and someone will mention that they are looking for what you do and due to the great project experience and the recent phone call you will be on their radar. This is priceless.
Glad to chat more just drop me an email on firstname.lastname@example.org if you want to share or chat.