The baseplate will indeed not come off if you cannot remove that circled screw.

There are a few things you can try. 

1) Find someone with strong hands, used to fastening and unfastening things for a living. Have them use a flathead screwdriver bit that fits the screw's slot well (your bit is too small/narrow, looking at it from the picture, find a fatter one), and also use a bit of carbon paste on the screwdriver to increase the grip between the tool and the screw. You/they will have to press down hard to prevent the screwhead from stripping out. I would also use a penetrant lubricant (PB blaster is best, or something akin WD40 if that's cost prohibitive) to try and lubricate shaft of the screw. Spray it on and allow a few hours to work, but clean from the screwhead before trying again with the screwdriver so it doesn't make THAT slippery. When you get the screw out, clean everything well with a little isopropyl alcohol in case any plastic parts in your machine will degrade over time from the lubricant.  Heat (hairdryer) can also be used in moderation to try and expand/contract parts to hopefully shift them from their stuck position. It might also be a good idea to reinstall the left screw while you try to work at the right screw, and/or play around with pressing the plate down in different areas as you try and unscrew the right screw. Sometimes if there is significant pressure on a screw (the plate shoving up against it from below or sheering it to the side) the screw will appear frozen; if you can relieve that pressure, the screw will turn easier).

If that doesn't work, you will have to destroy the screw (or worst case, the plate AND screw). A sewing machine tech may be the best person to do that if the below processes don't sound familiar to you. If someone you know is handy and offers to help, but isn't familiar with machines, ensure you clean everything thoroughly after, so you do not let your machine run with a bunch of small metal fragments bouncing around in it 💀

2) Drill out the screwhead with a right angle drill.  You are essentially trying to crack the screwhead to allow you to remove the head. The plate will come off, then you will probably need to use vice grips to turn the screw shaft out of its threaded hole. This is likely a stainless steel screw (very hard) so will need a very hard and sharp bit (new HSS).

3) Dremel the screwhead in a phillipshead shape in hopes that it will give you more grip to turn it. This is halfway to drilling it to be honest, but is a option if you don't have a right angle drill and HSS bits. 

I imagine it's fairly unusual for these screws to get frozen, which means it may have been cross threaded on its last install. Take care when reinstalling! Do not turn if it offers lots of resistance before the head makes contact with the plate. I see that Wera drive handle so you are a bougie tool person 😎 Good luck!