Why do you suggest hourly? I understand fixed big puts all of the risk on you, but would you also consider daily or weekly billing as a reasonable compromise?
Larger clients are not flexible about how you bill them. Hourly is the only option. Never mind that you might be working on multiple projects, run training, meetings and so on
In this case, I would still break out my work across multiple projects and types of work all charged at the same rate. If no other reason than to give me a breakdown of numbers to estimate future projects.
Billing hourly or daily is about the same. Weekly gets complicated. It is all about reducing risk, locking in cashflow and getting compensated for your time and energy.
Weekly/Monthly billing means you can never take a vacation. And if you're going to suggest pro-rated weekly billing well that's just daily or hourly billing isn't it?
You could certainly take week-long or month-long vacations, or take a month off of consulting to do things like business development or education. Generally, if you're at the level where you're billing engagements weekly or monthly, monetarily you don't need every single week to be filled with billable work.