While this may not work for everyone, I was able to get all of my veterinary hours by working at animal hospitals. It may vary by state, but in California you don't need to be an RVT to do technician work (although some skills are off-limits). I started working as an assistant with no experience, and worked my way up to the technician level while going to school. This allowed me to earn money while I was getting my hours (double whammy!), and gave me TONS of experience.
I know in some hospitals, employees are hired specifically to do kennel/cleaning duty, and it can be difficult to break into "veterinary" experience. I started working at a smaller hospital where the techs did all of those things, and the entry level position entailed assisting the technicians.
The money isn't great, but I really value the fact that I have been able to be so intimately involved with the hospitals I've worked at. On the other hand, I've never actually "shadowed" a doctor, so I can't really weigh the pros and cons.