I actually think all the information you received is correct, depending upon the context.
You do NOT get a point BEFORE you are unsuccessful in a draw. The point is awarded AFTER the draw is complete and you are unsuccessful. You either get a permit, or a point, not both. So if you have 16 points and are applying, you don't have 17 points. You only have 16 points. But you also have the current application, so it would be 17 total. 16 of those would be from points, and one would be the current application.
After the 50% of bonus tags are awarded to the top point holders and the other 50% are going to the entire application pool, I do not believe the draw is not conducted a second time. They simply draw from the lowest remaining numbers until all the permits are allocated. This is probably why you were told that it is only 1 try. Every application, whether it is a current application or a point, is given a number. The lowest numbers draw the permits. And since a person may only draw one permit, only their lowest number in the draw matters. So while you still had 17 opportunities in the draw, only your lowest number given was used to determine if you drew a permit or not.
So if I was applying for a hunt that had 100 permits, 50 of them would go to the top point holders and 50 would go to the application pool at large regardless of what points they have. Say I have 4 points (plus a current application, so 5 total), and the numbers my permits were assigned were 17, 31, 758, 903, and 5,657.
Only my app with number 17 assigned would be used. Even though 31 would technically draw a permit, I can't get two permits, so only one number is used.
This is a very simple breakdown of how it works, and how in context, depending on your question and also how your question was actually understood, could make all the answers you received "technically" correct.
To answer your question, you get as many tries in the hat as you have points, plus your current application. And only the your lowest assigned number matters in the draw.