Bill,

I wonder if these were bedded in something other than silicone.  I would stay away from the power drill.  To many opportunities for an accident.  I'd try putting the screw driver in the slot and rapping on the end with a hammer and then giving it another twist.  I have also had luck on occassion gripping the shank of the screw driver with a pair of vice grips.  You can put lots of weight into keeping the screw driver down in the slot and get added torque with the vice grips.  I would think some combination of the above will get them loose.

Good luck and hopefully some other folks will have some good ideas.

Paul

Since the goal is to refinish the deck you could just cut the heads of the screws off with some sort of cut off wheel, dremel maybe. Then pull the loops off and grind the screws flush. Much care would be needed in this tho. 

Then you could reinstall the holddowns next to the old screw or move them and have a bright spot.

My experience with old hardware (automotive) is that it will probably snap off any way. Cutting them all might give you a more uniform look.

Dan 

When I was installing my deck hardware, I broke off one of the screws.  I pulled out what I could.  Then I filled the remaining hole with thickened epoxy and sanded it flush once it had cured.  I drilled a replacement hole right next to the broken screw, installed a second screw, and it looks great.  I used to get hung up on everything being exactly in it's place, but no more.  An offset the thickness of the screw is ok with me.

if you have access to an impact driver (very popular for cordless drivers), use that.  It tends to unstick stuff well, better than a hand held screw driver or standard drill.  But be prepared for the screw to break.

I'm wondering if applying heat to the screw would melt any glue/epoxy stuck to the treads?

Phil 

Yes, I'd try applying a soldering iron tip to the head of the screw.  If it's epoxy that has a grip on it, it shouldn't take much heat to free it.  -- Grant