Draining grey water into septic from below 1/4" per foot grade

Hello,

We have a shed where we're installing a washer, sink and shower. The shed can't be raised up a from it's current location which is below a 1/4 inch per foot slope grade.

On solution I thought might be feasible is to drain the water from the washer, sink and shower into a plastic container installed below ground using a 2-3 inch drain pipe and then pump the grey water using a sump pump into a 4 inch septic drain (going to the septic tank) approx. ~15 feet away.

All of our 4 inch septic pipes were installed at a 1/4 inch per foot slope. However the shed drain output there's no way to install that sort of slope as it's below that grade. I believe even if we installed our own drain from the shed to the septic tank we could not create a 1/8 or 1/4 in per foot slope. The shed and the ground it's on appears to be below the septic tanks inlet.

Any thoughts about getting grey water to the septic? tank with sump pump feasible? We do have a 65 gallon plastic barrel tank and a 200 gallon rectangular tank. Seems that 65 gallon tank should be enough?

What sort of HP and GPH should the sump pump be? Our septic tank uses one of those non pressurized infusion drain fields with septic leaching chambers and not the pit with gravel type.

Gray water doesn’t take much of a slope. Brown water needs the steeper slope to maintain velocity and carry the solids. But the minimum slope is changing, because newer low volume toilets will have the solids falling out due to the low water volume.

there are small lift stations out there zoeller makes them little giant is another brand best way to size is talk to a rep and tell them what your using it for....I have one in my basement I think its 37 gal I forget the pump size but its a grinder pump for (solids) you should also mention the type of septic you have