Try lanoline  - available at drug stores. Somewhat expensive - 2 Oz is about $ 13.00.
How old are the rubber parts. If it is hard to pump sometimes it is the joker valve.

I plan to use ​silicone valve grease.

Is silicone grease safe for potable water?

Both are silicone based, both are safe for use with potable water. ... Silicone grease is commonly used for lubricating and preserving rubber parts, such as O-rings. Additionally, silicone grease does not swell or soften the rubber, which can be a problem with hydrocarbon based greases.

https://www.homedepot.com/p/Super-Lube-3-oz-Tube-Silicone-Lubricating-Gr...

Once a year, I do what you do but use vasoline. Then, whenever we pump out I will use head lubricant from WM. When out cruising and it seems to be getting tight, I would use baby oil or more head lubricant to loosen up the pump action.

Super Lube inside the pumping chamber is recommended by Head Mistress Peggy Hall (seconded by me). Her book on heads and boat odors is a treasure trove of good info. https://www.amazon.com/Get-Boat-Odors-Peggie-Hall/dp/1892399156/ref=mp_s...

I keep a small bottle of mineral oil usually buy at the dollar store add a bit, pump a few times and allow to stand shortwhile works every time