FYI the whole purpose of the alignment is to make the HC internal star map match the sky. The first alignment star will be a ways off of true and all you need to do is use the HC to move it to the center of an eyepiece or camera display. To change slew speeds use the rate button on the HC. Its one of the numbers. Simply hit rate, then choose a number from 1 to 9 (9 being max, 1 being guide rate) and hit enter. Once the star is close use the rate button again to slow the rate so you can fine tune it.
Couple of things you need to be sure of if you are not using a GPS module:
1. Date and time are correct for local time.
2. Daylight savings (DST) is set correctly.
3. Time zone is correct.
4. Location coordinates are correct. As an example, i live in Dallas Texas area so for me the coords need to be in the North west hemisphere. My controller usually defaults to North East for some reason.
If all these are correct and PA is accurate as you stated then the scope should move the mount to near but not on the first star. Align this then choose the second star. It will move closer to that one. if you do a 3 star it will be closer still. once all three are done the scope should be able to get any object in he field of view though it may or may not be dead center. The first alignment star is always the most inaccurate though it should not be off by a really large amount. If it is then usually something you entered in the initial setup phase was wrong. If you are using a GPS module then Time/Date/Location will not be entered manually as the GPS will pick all of that up directly from the satellites. You will still need to set DST and time zone correctly.
Note: 1 star alignment is good for quick and easy alignment of a single small area of the sky but should not be used if you are going to do anything more than visual and not for farther away objects, for that do at least a 2 star alignment.