Yes, back off the adjusting nuts ,loosen both cables from their perch and remove them from the carb.
Badly varnished pins and such don't take kindly to brute force or hammer tapping. Try a hairdryer before force. heat up the area on the carb you're working on , it'll loosen up the varnish, may take a few trys to get it working freely , keep the heat on it and remove the parts gently.
Do not use a screwdriver to force slides open.Use hairdyer again or soak in carb cleaner.
Use hairdryer in the pins too, for a while, this may require a light tap with a loose pin to get it sliding or a brass needle from your slides( you'll need a rebuild kit anyways) Tap very lightly use penetrating oil and heat to make it slide, no hammering.
If you want to see the piston move why not take the plugs out and bump it, or turn it by hand on the generator side. Was this engine ever seized once before?
Save the starter and battery till you have some clean carbs back in her, that will be worth the wait, You can hear it run then.