My first Solo Distance Sail

[seasalt2012]

Howdy Yáll,
I am the proud owner of a Bayfield 25. A great little boat, lacks on speed but makes up for it with good looks and seakeeping ability. I am planning on vacationing to Pensacola, Florida in the spring... and would not mind having my boat there! Most likely just a long weekend type deal.
Anyways, I have ample time off, my fiance'not so much. So, I'll be doing a solo sail all the way there. Its about 110 miles from my harbor to the Condo (with pier and boat slip provided), so at roughly 4 knots that is about a 27.5-28 hour sail.

2 options- ICW or coastal. Both are the same option really until you hit Mobile. Then the inland ICW picks back up.

I can easily stay awake that long but would need a big nap when I get there, and I would rather hit the ground running. My only electronics are a chart plotter, depth finder, radio, an an auto-tiller. The water pump is electric for the motor and ran off the battery. The previous owner rigged this up and it seems to work well.

I have never ran them much due to the fact that I am terrified of running out of battery power to start the engine if needed. I have a single deep cycle battery and a single starting battery, with the alternator charging both. Also, a single solar panel just in case (never really had to use it).

Do you think I can run the auto-tiller for a certain amount of time while I catch some shuteye?(30 mins max). I figure I can see 2 miles, and determine what obstructions and/or traffic are ahead. I'm mostly worried about running out of battery power, and getting off course.
Do you have any other advice for me? I appreciate the help!