Ken,
The budget you are quoting for the hardware specs you need, would be attainable maybe with a unmanaged budget host, but is not realistic for a truly quality host as you state you're seeking.
If you want more than 20 on-site techs, you've ruled out more than 95% of the data centers/providers out there. Really, you're down to about 5 or 6 left, and rackspace -- who is outstanding and not at all overpriced -- is one of them. I should also point out that if they have 20+ on-site techs, you are now in the realm of company where as a customer, you are "just a number," one of masses at a server farm. If you don't mind that, cool, but you're not going to get any continuity of service. Every time you open a ticket, it's going to be a different tech, and they're going to have no idea what was done 5 minutes ago, 5 days ago, or 5 months ago. You will need to explain everything over from scratch because they don't read ticket history. If you want personal and attentive service, to be remembered by your techs and treated like a person, a huge host is not going to be able to meet those expectations. I've hosted at a couple of those places

trust me, been there/done that/experienced it firsthand...
As I eluded to above, Rackspace's reputation and prices are entirely earned and well-deserved. $600/mo. for 300 GB top-quality bandwidth, and for the level of redundancy, support and service they offer, is completely par for the course. Ken, if you are truly looking for "high-end, superb managed hosting" -- rackspace is your ticket, and that's what high-end superb managed hosting costs. It ain't cheap. Just as you want to be paid fairly for your time and expertise, that's the rate that the high-end "superb" full-managed hosts charge. Cadillacs don't have a Honda pricetag.
Next question, you mentioned 50 IPs... why do you need 50 IPs? Do you have 50 SSL certificates? SSL certs and personalized nameservers are the only two technical justifications for a dedicated IP on a site, according to
ARIN, which is the organization which doles out IP addresses. You are not going to find a
reputable host who just hands over 50 IPs for sites that don't have a technical justification for them. If the host says "sure, no problem" and hands them over -- that's a
big red flag -- run, run away!

Now if you have 50 SSL certs, awesome. But otherwise just that you're running a particular file type (videos) is no reason the sites can't (or shouldn't) go on a shared IP. The sites
should be on a shared IP. CIHost's practice of allowing customers to waste IPs only means (a) they are wasting IPs, and (b) pain for customers down the road when they must be dragged kicking & screaming to the industry-standard practice of using shared IPs. It's really a shame they are doing this.
Ken, what control panel do you need?
What kind of CPU power do you need? Are you just pushing videos (which uses little CPU time), or are you also crunching data, doing high-volume SQL queries (like running forums)?
What kind of data volume are you pushing, mbit/sec? I'm wondering if you need a standard 10 mbit/sec connection, or a 100 mbit/sec card. The latter costs more, but the result is that if you have a surge in traffic, your server is not stifled by the speed of its network connection.
Do you need a backup service? A 2nd drive for backups or do you use an off-network/3rd-party provider for your backups?
What level of management do you need? Most "managed" hosts, aren't actually managed. 99% of them are reactive and only do work when you request it. That means you still need to know enough about running your server to know what is installed, know when exploits have been identified on that server software, and therefore know when to ask to have it updated. That's not very managed, eh?

So don't just go by the tag "managed," because that is a word which is not defined in the industry. Anybody can claim managed, and it means basically nothing. You need to dig into their SLAs to see what exactly they do, when they do it, how they do it.
Ken I hope this helps.

These are all great questions to ask a prospective host. Picking a
good host isn't easy, especially for a layperson who doesn't know much about hosting... I liken it to me trying to buy ... power tools. I wouldn't even know what features to look for, or what to ask about, in order to compare the models the right way and make a good choice?? So I would ask my friend who is in construction to help me pick out a good model. Please think of me as that "friend in construction" (well, web hosting)

I truly hope that this has been helpful to you.

Bailey