Hi Graham,
Thought i might be able to share some facts about this, having been through quite a few showreel and application processes recently!
getting a green light from a major studio to use their footage is not very likely
Not always true in my experience. I did a showreel a few years back with some Universal footage. Youtube have a copyrights policy. You can indicate material is for educational or demonstration purposes. They contact the copyright holder and seek permission. In this case i was granted use. It took about 2 months to clear. Something i learnt from this experience, host your own video, its quicker.
In my experience, a copyrights holder will only pursue a claim when an interested party is making money from distributing their stuff. If no money is being made, then its usually as waste of peoples time.
they will not allow me to post any work that I did for them on my site or in any reels for self promotion
This sucks big time, and the whole excuse of 'we don't want people to be confused' is rubbish. I work with a lot of different companies on separate projects, all of them outsourced. There is no confusion to create when its quite clear that an individual is working for a studio directly. Providing this is stated clearly in your credits I'm not exactly sure what they have to gain here, apart from a poorly executed staff retention policy.
You should be credited publicly for your work even if you can't sample it. If this is the case i would point people towards official youtube footage of the game and also IMDB credits etc. There should be plenty of information publicly available that relates to your work. If you are credited, theres no reason you can't use this as links.
Also a few points relating to how useful showreels like this are. I would agree and say the have limited use, but its down to how you execute the whole thing. Example, if i want a job at studio X i look for showreel footage to use from that studio. I make it sound pretty badass then send it back to someone who is an audio decision maker at that studio. Someone who creates (and cuts!) the jobs around there. Someone who can take action.
If i did a showreel with loads of really nice looking footage from huge hollywood films I'm sure it would sound great, problem is i don't really apply to jobs in LA and i don't do a lot of work on film mix stages. I work in games largely, so i pick footage that serves this purpose. Having multiple showreels that drag on demonstrating a ton of different stuff is also something i have learned to avoid. My personal rule is no more than 1 minute and make it feel like a finished product.