Your understanding of the effect of BCAA's on serotonin is not 100% correct. Let me preface this with "I am not a biochemist", I'm learning like everyone and if anyone who has a degree could improve my answer, please do!
Lets get some science up in here.
Branched Chain Amino Acids (BCAAs) refers to three amino acids: Leucine, Isoleucine, and Valine. Leucine plays an important role in muscle protein synthesis, while isoleucine induces glucose uptake into cells.
The central hypothesis of fatigue (which assumes that elevated serotonin concentrations in the brain are associated with induction of fatigue 1) is thought to be related to the anti-fatigue effects of BCAA supplementation.
During exercise, the plasma ratio of aromatic amino acids (tryptophan) to long chain neutral amino acids (the BCAAs and a few others) is altered in favour tryptophan  due to BCAAs undergoing oxidation and being destroyed , and due to tryptophan and BCAAs sharing the same transport into the brain  and this act of transportation is the rate limiting step  any alteration in the ratio will alter what amino acids transport into the brain, and exercise has been confirmed to increase tryptophan uptake in as little as 30 minutes and increasing tryptophan availability via supplementation (without supplemental BCAAs) appears to promote fatigue in rats.
Increased tryptophan transport into the brain (which produces serotonin via 5-HTP) is a possible causative factor of fatigue, and replenishing oxidized BCAAs to preserve the ratio can attenuate fatigue production.
Supplementing BCAAs prevents a serum decline in BCAAs, which occurs during exercise. A serum decline would normally cause a tryptophan influx into the brain, followed by serotonin production, which causes fatigue.
Exercise raises brain serotonin release and is postulated to cause
fatigue in athletes; ingestion of branched-chain amino acids (BCAA),
by competitively inhibiting tryptophan transport into brain, lowers
brain tryptophan uptake and serotonin synthesis and release in rats,
and reputedly in humans prevents exercise-induced increases in
serotonin and fatigue. This latter effect in humans is disputed.
Branched-Chain Amino Acids and Brain Function J. Nutr. June 1, 2005 vol. 135 no. 6 1539S-1546S
- Ament W, Verkerke GJ Exercise and fatigue . Sports Med. (2009)
- Davis JM, Alderson NL, Welsh RS Serotonin and central nervous system fatigue: nutritional considerations . Am J Clin Nutr. (2000)
- Blomstrand E A role for branched-chain amino acids in reducing central fatigue . J Nutr. (2006)
- Blomstrand E Amino acids and central fatigue . Amino Acids. (2001)
- Blomstrand E, Celsing F, Newsholme EA Changes in plasma concentrations of aromatic and branched-chain amino acids during sustained exercise in man and their possible role in fatigue . Acta Physiol Scand. (1988)
- Fernstrom JD, Wurtman RJ Brain serotonin content: physiological regulation by plasma neutral amino acids . Science. (1972)
- Fernstrom JD, Faller DV Neutral amino acids in the brain: changes in response to food ingestion . J Neurochem. (1978)
- Pardridge WM Blood-brain barrier carrier-mediated transport and brain metabolism of amino acids . Neurochem Res. (1998)
- Blomstrand E, et al Effect of carbohydrate ingestion on brain exchange of amino acids during sustained exercise in human subjects . Acta Physiol Scand. (2005)
- Nybo L, et al Neurohumoral responses during prolonged exercise in humans . J Appl Physiol. (2003)
- Meeusen R, et al Effects of tryptophan and/or acute running on extracellular 5-HT and 5-HIAA levels in the hippocampus of food-deprived rats . Brain Res. (1996)
So?? Too many long and complicated words, make it simple!
Imagine the bus lane on a road going into town. Buses and taxis can use this lane but they cannot occupy the same space at the same time (without crashing).
Tryptophan Bus Company and BCAA Taxis are working the rush hour...
At the start the ratio is fairly even. Rush hour hits and lots of taxis are required, leading to the buses being inhibited from entering town. Once the taxis run dry the ratio swings back the other way with buses filling the bus lane. The result is after rush hour there are more buses in the lane meaning that you are tired (but happy!)
The following day...
BCAA Taxis supplement (get it?) their fleet by hiring more cabs. Rush hour hits again but instead of taxis running out really fast and buses clogging up the bus lane the ratio of buses to taxis remains constant through the period. The result is that after rush hour there is no imbalance in the ratio between Tryptophan and BCAA transport.
What should I take to offset the reduced serotonin?
You shouldn't, accumulated knowledge suggests that:
[Regarding BCAAs] In regards to the anti-fatigue effects, it is highly
plausible that this will only apply to untrained or lightly trained
persons doing prolonged exercise. There does appear to be a difference
between trained and untrained persons, and perhaps this is due to less
tolerance to exercise-induced sedation (fatigue tends to set in
earlier in newbies, so an anti-fatigue effect is going to affect them
My personal recommendation is, READ UP ABOUT THEM. Try them out for 3 months, if they help then keep taking them, if they don't then stop. You should get enough of them from your diet if you are eating 1-1.5g protein per lb bodyweight per day.