The part where I have a difference of a opinion is here:
> I've found that there are quite a few companies that can pay me worthwhile contractor fees yet cannot budget to have a UI guy, a backend guy, and a product manager as employees.
Specifically, the definition of 'worthwhile contractor fee'.
The average ho-hum web developer with a few years of experience, the LAMP stack, JS/HTML/CSS who can tell the difference between an abstract factory and an anonymous function in London can easily pick up a £250-£350 ($380-$540) per day contract. I would fall (just about) into this category. This however is not the type of engagement I believe the OP was talking about, and not what I was referring to when I said 'worthwhile contractor fee'.
The sort of fees I was referring (and I believe the OP is referring to also) to are going to be about one order of magnitude higher than the amounts mentioned above. Hypothetically, imagine what sort of fees you'd be paying John Resig or David Crockford to consult on your organizations frontend code, or DHH to consult on Rails, or Steve Souders to consult on frontend performance, or Chris Shiflett to harden your PHP apps security.
While the examples I've given their sound like special cases of internet celebrities, there are really real people making a happy living doing this sort of work at very high (i.e. 'worthwhile') rates. I personally know of technical contractors who are paid more than £1k/day (specifically in database performance, and website conversion), and thats just within my immediate circle.
On the other side of the fence, at one one of my previous companies (which wasn't that big, 30-40 staff) we had a team of developers with QA, a separation between front/back/sysadmins, but no one with dedicated database performance experience/skills. We had budget for (and would have gladly paid) something like £10k for a database performance specialist with good references to come in for a week or two, show us what we could do to make our db perform better at scale and establish some best practices for doing things right going forward.