What can be done to avoid being unable to perform the five daily prayers after marital intimacy, despite immediately performing ghusl and reciting adhkar, which leads to abstaining from intimacy for long periods in order to preserve the prayers?

This is from the deception of Satan, for there is no connection between marital intimacy and abandoning prayer. You must repent to Allah for abandoning prayer, as it is one of the greatest sins. You must realize the seriousness of this and Allah's wrath. Cast away these satanic thoughts, associate with righteous people, and reflect on death and what comes after it. It is not permissible to abandon marital intimacy with your wife in a way that harms her, as it is obligatory according to ability and need. Strive in supplication, asking Allah to help you fulfill your duties.