By the time they'll be in there, the media will have run for about 3+ months, am I right in thinking this will have the desired effect?
Well I suppose that depends on the desired effects
.
By putting in the extra biomedia you are increasing the available surface area that the nitrifying bacteria are able to colonise. As long as it had a good amount of flow over it and doesn't clog with waste it should provide that.
However, bacteria like everything else can only survive if there is enough stuff to live off. So in theory that media is able to look after that amount of fish, when you transfer it to another tank it still is looking after the same amount of fish. When you go to add more fish, the numbers of bacteria are able to increase as there is more waste to live on. that's why it is good practice not to add too many fish at once.
That being said, when changing tanks you are losing all the bacteria which have colonised the bits of the tank which are not coming into the new tank eg glass so in theory it can provide that important buffer space
Is there such a thing as too much media?
I mean its complicated, how much surface area hold enough bacteria to support the waste conversion of 1 fish?
Take part of this abstract about the mechanics of nitrate production in RAS systems;
"Expressed as volumetric total ammonia-N (TAN) removal rate, the MB filters had significantly higher removal rate (231 ± 17 g N−1 m−3 d−1) compared to the FB filters (92 ± 2 g N−1 m−3 d−1). Expressed as surface specific TAN removal rate MB filters had significantly lower removal (0.27 ± 0.02 g m−2 d−1) than FB filters (0.46 ± 0.01 g m−2 d−1). When conditioned to a higher inlet TAN concentration (6.27 ± 0.39 mg l−1) for 2 weeks, the FB filters increased the removal rate (146 ± 3 g m−3 d−1 or 0.73 ± 0.01 g m−2 d−1) while the MB filters had unaltered performance. The results indicate, that the more heterogeneous and stratified biofilm to be expected in FB, can react more flexibly when challenged with changes such as differences in TAN loading. The effect of dissolved oxygen level on FB filter nitrification rates was additionally tested at TAN 5.35 ± 0.06 mg l−1. Below approximately 60% saturation (7.1 mg O2 l−1) measured at the filter outlet, nitrification rates started decreasing rapidly. "
Suhr, K. I., & Pedersen, P. B. (2010). Nitrification in moving bed and fixed bed biofilters treating effluent water from a large commercial outdoor rainbow trout RAS. Aquacultural engineering, 42(1), 31-37.
This will then obviously change between temperatures, feeding regime, loadings, DO, plants/algae, type of biomedia, age of biomedia ect.