I am in a similar situation to you, and I also have propane tank. I am currently heating my house with propane, but I would like to utilize the methane which I am already generating.
Here is a comparison of a septic tank and a digestor.
I believe that with a few modifications a septic tank could be turned into a continuous loading bio-digestor. I am a believer in grey
water, so I will route that out of the tank, but the black water could be routed through some kind of a one way valve and into the tank. Then a piece on the top could easily be added. Even through the access hole. another one way valve could be used to allow methane to exit and be guided into a bag for storage. The bag could be used as is (with a weight on top) or in my case, I would like to run the gas through a compressor and into my propane tank, which is already fully hooked up to the house. I have been considering the possibility of using an old mechanical compressor from a car AC system and run with an electric motor. This compressor could be turned on when the bag is full, and the methane would be injected into the metal tank.
I do not think that the waste must be mixed before it enters the digestor, but this process does aid in breakdown by the microbes... but just about every biogas system uses the mixer, so it would be easy to route the black water into a mixer which would then flow into the digestor. I would prefer that the mixer is automatic, but it could also be manual. An automatic system could be as simple as a 50 gallon tank which has a float switch on top. When activated a motor moves turbines and blends the waste. then it would be flused into the system. By the way if this is what you are trying to achieve, then obviously antimicrobial
soap, and many other toxic chemicals cannot be allowed to enter the digestor, as this will kill the
dragon.
As a septic tank is so similar to a continuous anaerobic digestor then there are many different variations on continuous digestors as from
wikipedia "In continuous digestion processes, organic matter is constantly added (continuous complete mixed) or added in stages to the reactor (continuous plug flow; first in – first out). Here, the end products are constantly or periodically removed, resulting in constant production of biogas. A single or multiple digesters in sequence may be used. Examples of this form of anaerobic digestion include continuous stirred-tank reactors, upflow anaerobic sludge blankets, expanded granular sludge beds and internal circulation reactors."