I think on that I've just been using the Silicon Spray from Walmart.
If the plunger doesn't move easily after spraying, the blade is having a hard time getting through the rubber seals inside the valve. You might try a combination of vegetable oil and Dawn detergent added through the toilet - maybe a cup of each. Let it sit for a few minutes. Spray the Silicon Spray into the sewer outlet - it may have to go a few feet, so be liberal. Put a bucket under the sewer outlet and exercise the pull handle rapidly to work the oil/Dawn/spray into the valve. Let us know the results.
Dave's suggestion on a piece of wood to hold things in place is a good one.