Hard to Remove PM 2.0 x 3.0 Battery Hold Down Screws

Laptop is my daughter's HP Spectre 13-ac000 x360 Convertible PC, 
purchased in March, 2017.  Some years ago (sorry, I don't know when) the 
laptop was giving "extreme low battery" warnings, and eventually wouldn't 
hold a charge, but it would boot up when using the charger.  Finally, the 
laptop wouldn't boot up even with the charger.  My daughter then put the 
thing in her closet and bought a new laptop. Yikes.

She brought this up to me today, and I said let me see it.

I plugged it in, and the orange charging light went on.  An hour later, 
the charging light turned white.  Ok, guess it's charged, but it still 
wouldn't boot.  Nothing, not even a hint that anything's going on inside.

Per troubleshooting advice, I pulled the charger, and held the on/off 
button for 30 seconds.  Plugged the charger back in, but still wouldn't 
boot up.  Troubleshooting suggested that the battery may be the cause and 
to remove battery and try again with just charger and battery removed.

So I got the manual:

http://h10032.www1.hp.com/ctg/Manual/c05357578.pdf

I got the back panel off (had to use a hairdryer to get the adhesive 
attached plastic caps off under the rubber feet, where the last two panel 
hold down screws were), but I can't get the PM 2.0 x 3.0 screws removed 
to get the battery out.  They are in there very, very tight.  I have 
tried very, very hard, with lots of pressure.  I just can't budge the 
screws here.

https://postimg.cc/bZ70k20R

I've always used jeweler's screwdrivers to do this type of work.  Would a 
computer technician screwdriver set make a difference?  Are the  points 
shorter to get tightly into the short depth of these small screw heads?

TIA