In statistics references I have read that H[0] should always be specified as "=" even if "≥" or "≤". I assume that in my case testing "=" is the same as testing "≥" since it is a one-tailed test?

This is just personally how I understand hypothesis tests; I'm not going to dispute your texts. But the way I determine if it's a one- or two-tailed test depends on H[0]: If H[0] specifies "=", then you must do two-tailed test. Do a one-tailed test if it specifies "≥" or "≤".

Hypothesis testing follows a procedure of

1) specify the null & alternative hypotheses

2) collect sample data

3) test the data, to determine if null hypothesis is accepted or rejected.

I think that hypothesis tests must present an either/or situation. So if H[0]: p1 = p2, then H[a] must be: p1 not equal p2. So then you collect data, and when you do your test (which would be two-tailed, because of your H[0]), it would be possible to reject the null hypothesis if your sample data has p2 > p1. Which is not quite what you want (you want to test if there is enough evidence to say that p1 > p2)