Two big thumbs up for pair.com!
The first host I tried looked pretty good, even with a $6/month charge for a dedicated IP address. Then I tried to upload my site using rsync. Nope, rsync is only allowed on their VPS or dedicated servers. Bye Bye.
Sent emails to a bunch of hosts that I could find (some only do chat) listing my requirements:
shared hosting
linux
dedicated IP address
rsync use
ssh access
ssi (server side includes)
access to raw log files
A lot of them responded that I needed to use a VPS or dedicated server; overkill for my 3 little web sites. But pair.com replied that everything I needed was covered in their shared packages including a dedicated IP address. Signed up for package 1 (7.95/month or 7.55/month if paid yearly). So far so good. SSH works, rsync works, lots of knowledge base articles. Very happy so far.