They way you are describing these events is far too black and white -- they really occur over a continuum. When I use the word "drain", I don't mean "deplete", but rather a reduction in the amount.
Let's take a step back and approach this from a different perspective. MAO-B, the MAO subtype classically thought to be responsible for metabolizing dopamine, is not very efficient at metabolizing serotonin. Strangely, however, MAO-B is the primary type of MAO found in serotonergic neurons. The reason why that is thought to occur is that small amounts of dopamine are normally taken up by SERT, and the MAO-B is expressed as a way to protect the serotonergic neurons from being damaged by dopamine. So it is a normal occurrence for dopamine to be taken up by serotonergic neurons. There are other mechanisms that exist to protect serotonergic neurons from dopamine -- pathways exist to limit damage due to oxidative stress.
What MDMA seems to do is impair several of the mechanisms that normally help to prevent serotonergic neurons from being damaged by dopamine:
Normally:
1. There is only a limited amount of dopamine spillover from dopamine synapses because release is regulated and excess dopamine is taken up by DAT. But MDMA blocks both of those mechanisms.
2. The ability of SERT to transport dopamine is limited by the fact that SERT has higher affinity for serotonin and because there is usually much more serotonin in the vicinity of SERT compared with the amount of dopamine. But by depleting serotonin, MDMA increases the amount of dopamine that is able to access SERT.
3. Serotonergic neurons are resistant to dopamine-induced oxidative stress. But factors such as MDMA-induced hyperthermia degrade those protective mechanisms.
Those events occur along a continuum. There may be some depletion of dopamine after administration of MDMA or a combination of amphetamine and MDAI. But if there is even slightly more depletion of serotonin then dopamine then that would potentially increase the amount of dopamine that is transported by SERT.
TPH inhibition isn't really a cause of the neurotoxicity -- TPH inhibition itself isn't neurotoxic. It is merely one factor that appears to contribute the neurotoxicity.