We installed a stack pack with a new main this past spring.  You might want to also consider adding a Tides sail track system as well if you don't have it already.  It makes life SO much easier raising and lowering the main - especially for lowering, as the whole main will drop down right into the bag as intended with no friction. Some comments related to your questions:

1.  I too have a dodger, and it definitely adds a challenge to zipping the bag up.  I found that by adding a long piece of parachute cord to the zipper (about 24"), I can start the zipper from the cockpit (maybe 2 feet or so), then flip the cord up toward the mast so I can reach it from forward of the dodger, then finish zipping from the cabin top.  This makes it super easy.  Your stack pack bag may even already come with a long zipper cord on it for this reason.

2.  Battens.  Yes, the battens can get hung up on the lazy jacks when you are trying to raise the main.  I have found that it is much easier to jump the main halyard from the mast than to try to raise the main from the cockpit.  This is especially helpful when you have a dodger, since maintaining visual contact with the main while you are raising it is impossible from the cabin top winches.  I raise the main 90% of the way at the mast, and then finish it from the cockpit winches.  This way, if the battens do get stuck on a lazy jack line, you will see it right away and can quickly lower the sail slightly to free the batten.  Also, if you are motoring right into the eye of the wind, I have found that the battens rarely get hung up in the first place.

My two cents.  Good luck!
 

Michael,
 We do have a Doyle Stack-Pac and it is about seven years old. In a word - it's great !
We also have the Tides Sail Track and I would certainly suggest you get one of those. Those two items have added years to my sailing carrer. The ease at which the sail goes up and down is worth every penny.

 Now on to your specific question: 
Yes, you do have to lean over the bimini top to grab the zipper pull (tab) when closing the 'Pac' with the sail inside. Many of us have put a long piece of parachute cord on the zipper pull to facilitate an easier closing. HOWEVER, if requested;  Doyle will make you a zipper pull so you can zip an unzip the long zipper from the mast location. You can probably make it yourself a lot less expensively. Here's how; 
 
This is a long piece of parachute cord that runs in a CONTINUOUS  LOOP the length of the Stac-Pac inside the lazy jacks - from a small block sewn on to the front side of the Stac-Pac (in the mast area) - down to a small block sewn on to rear inside of the Stac-Pac. The cord is then fixed to the zipper pull (tab) and operated very much like your window drapes cord. (I wish I had a picture) What this enables you to do is stand at the mast area an operate the zipper pull by pulling on the cord. 
(Hope that's clear) Anyway, it gets over the difficulity operating the zipper while hanging over the bimini. See https://www.youtube.com/watch?v=JMB-r4mtK1Q  On  youtube at point 1:08:34 for a clearer explanation.

The idea of standing at the base of the mast and 'jacking' the sail up  by hand  -so you can see if the battens are binding or catching on the lazy jacks - is the perfered method of getting the main sail up. You the finish taking it up the last few feet with your winch.
Not sure how handy you are with a sewing machine but Sailrite make kits of these stack-packs and you might want to look at those.

PS. Michael; You might want to put your location, sail number and year on the bottom signature line of your posts.
All the best,
Bill
 

Don;
Take a look at You-Tube at ​1:08:34.......Bill
https://www.youtube.com/watch?v=JMB-r4mtK1Q
 

My solution for getting the main past the lazy jacks is to use a winchrite in one hand and position myself at the back of the dodger with my other hand on the boom.  I can guide the sail by pushing the boom from side to side.   Others just listen the lazy jack and pull one side to the mast.   

when solo sailing I like to spend time in the safety of the cockpit   

Agree with the Stack Pack, Tides Track and Winchrite. To zip, I move the traveler all the way one side. I'm only 5'8" and I can reach to zip. I do have a short lanyard on the zipper.

Merry Christmas to all,
We have a Mack Sails, Mack Pack. The Mack Pack has a zipper closure running along the top length of it, connected to a continuous line running to the mast. We will usually unzip before we leave the dock. Raising the main we head into the wind and after the first two battens are clear the rest goes up fine.