No apology is necessary; we all get frustrated from time to time and you were not abusive in any way - just expressing your frustration. .
There are indeed different metrics for different situations. While generally I have had good response from DH ("good" meaning 1-4 hours, sometimes less and sometimes more), DH only claims to try to respond within 24 hours - and I'm sure that is all part of what allows them to price as aggressively as they do. In most cases, the delay in tech support response time is acceptable to me because of the value, but I understand that YMMV.
Shared host do have certain characteristics; I'm hopeful that, once this issue is worked out, you will find the occasional bumps in the road to be worth the space bandwidth - it's different for everyone. DH has been very good for me in spite of occasional problems - I've been here 8 years now, and find the performance/price ratio to be outstanding (though, like everyone else, I'm frustrated by the occasional glitch)
Welcome to DH, and good luck in getting some resolution on your speed issue.