Transplanting has nothing to do with plant health,i grow from veg all the way through the entire flowering period in 3.5 quart pots which is less than one gallon,plants being rootbound causing health problems is complete bullshit,a plants root system only need be large enough to deliever water & nutrients that the plant needs & no larger.
If your getting brown roots in a soil grow it is from lack of oxygen,no doubt about it,the main things that cause lack of oxygen in soil grows are having the soil in a constantly wet state,if it never drys out the plant cant breathe ,another reason is from compacted soil,and even another reason is from watering with water that has sat too long & becomes stagnated,yet another reason is too many amendments in the soil that retain water like peat moss,in large volumes it stays wet for long periods.
The over watering can be easily corrected by using much smaller pots,the whole 1 gallon pot for every month the plant is going to be alive is pure bullshit & causes more harm than good with new soil growers,i like my pots small enough(less than 1 gallon) where they need to be watered every other day when they are in veg & every day when they are in heavy bud,watering brings fresh oxygen to the plant.
Compacted soil can be corrected using perlite,not to be confused with vermiculite,perlite does not retain water & it keeps the soil loose so it can drain & breathe,adding masons sand to the soil helps alot as well just be sure not to use beach sand as it will kill your plants,vermiculite retains water leaving the soil moist for longer periods,even though it helps loosen the soil its not the best choice because of water retention,be sure to add atleast 20% perlite to the soil.
If your water sits too long before watering the plants it can become stagnant,much like a fish tank where the pump goes down the oxygen is depleted in the water,this can be corrected by adding an air stone to the water resivior if the water is going to sit for several days,adding small amounts of hydrogen peroxide also helps add oxygen to the water.
Having a loose soil mix that drains very good & drys out quickly should solve your problems.