A major undertaking...an entire overhaul of system, sans tools and resources, hey?
I feel and hear your pain. Been there...successfully, unsuccessfully, but always with some pain and ultimately, lots of growth personally and professionally. Gotta love it! I wish you all the best.
Using your bullets, what I see as the primary compelling needs are #4 and #6.
#6 - This might be impractical, but. There are tons of free - or very low cost - tools that you can use. My org is a not-for-profit, and this here economic recession they got going on has cut off 2/3s of our revenue stream (construction and local governments). We've just gone live with a new website that was built on free (open source) technology. We have a free CRM on the backend (sugar crm), and now can capture visitor data, run campaigns, get all sorts of report data, know who talked with whom, when, and what the outcomes were, etc. It was very difficult for boss-man to turn down "free."
#4 - I see this as a process flow issue...and perhaps a tighter methodology will help ease the pain. You control the process until The Big Boys step in, then you become the liaison/information gatherer and processor....? (My assumption). What does this look like on paper, all mapped out? What steps are taken? Are the steps the same for every transaction, or are there transactional variances?
Time is critical here ("need..to do more..., faster"), So if Point A is the very beginning, what steps are taken to get to Point B (the endgame), who is involved, what do your historical and anectdotal data tell you, and where oh where can you effect change to shore up the spongy spots?
If you map this out, good old fashioned paper and pencil (with a big eraser), I'm betting that patterns will emerge, ideas will flow, and you'll gain ground.
Michael, with regard to your #5...I don't know your situation, but my head is staying stuck on this one, so I'll do my best to capture my thoughts here without sounding like a total doofus.
Have you considered that this item is not best resolved by you, but rather by your support staff? I'll make some assumptions here that are probably fairly accurate: your staff know their jobs and how to get 'r done. That said, they know the tools and resources that are available, they know the systemic problems they need to overcome, and I'll bet dollars to doughnuts each of them have thoughts (valid or not, expressed or not) on improvements.
Money is not an effective long-term motivator. Being recognized as having value, however, is. Could you lay this problem at their feet (perhaps in some sort of structured manner), and give them the Captain Piccard: MAKE IT SO.
FWIW, staff who are jazzed can move mountains. Give 'em a project, and give them 'control' of their destiny. Sit back, offer guidance, and watch Stonehenge get built.
Just my two cents (devalued like my house, so maybe you can currently get 1/4000 street value) :-)