Not too sure by what you mean.... "time the flush" ?
Also... when you say .... "the 310 has a tendency not to let all the doo doo go down the hole" .
Not all...but a lot of the problems RVer's have with the 'flushing' of the RV toilet is that they do not use enough water 'before and during' the flush process.
Often there are sharp turns in the toilet drain that may cause a slowdown or sometimes a plug.
If the bowl has plenty of water prior depositing the 'doo doo' it then should have good lubrication and gravity power to pull everything through when you flush... along with the water that is flowing to assist the flush during this time.
It usually not recommended to leave the black tank valve open.
'Scotty... has a good point.'
Another Reason being is that the solids can pyramid and cause a bigger headache.
It is always best to drain the partially filled black tank after you have turned on the 'black tank rinse' and filled the black tank to almost full of water.
Then with the rinse still running... open the black tank valve...completely evacuating the black tank.
IMO... installing a house hold toilet wouldn't solve your wish to leave the valve open.
'07 WildCat 30 RLBS ~ West Coast Edition ~
Trail Air - Tri Glide Pin Box
2000 F350 DRW 7.3 Diesel Lariat 89k miles
Edge programmer, 4" SS exhaust turbo/back
Vancouver Island, B.C., Canada