There is only one feed inside the tank for drawing water, which then goes directly to the pump. No difference for shower vs. sink. Tank level is not a relevant factor IMO.
Guessing that using the shower with the valve/valves wide open [do you have separate hot and cold faucets in the shower?] is asking for more water flow than the pump can keep up with, thus the pressure drops. Try showering with lower water flow if possible, or put a flow-restricter in the shower head.
An accumulator will not solve the problem, just delay its onset IMO.
Most pumps have an adjustment screw which will let you change the "on" and "off" water pressures. [link below] If you can get the pump to turn on more quickly, it may have a better chance of staying ahead of the shower water flow IMO. Need cooperation from the bio-mass in the shower also . . .
Good luck, especially with the DH aspect!
PS -- Domestic Harmony!
PS2 -- If you click on the orange arrow in the following quote, you will go directly to that 2015 post in the 20-footer thread with details, photos and a YouTube video about adjusting the pump's pressure points. Not sure if this applies to your pump of course! FWIW
Originally Posted by OTRA15
On our 2014 FC20, the pressure switch is on the right end of the pump . . .
. . .
PS3 -- You could try to replicate this on city water, by closing down the hose bib, to get a low water flow when showering. Chances are good that you can. On city water you will have plenty of time to experiment, especially if your grey valve is open and the shower waste water is going down the drain.