Should a person afflicted with excessive pre-seminal fluid (madhy) be treated like someone with urinary incontinence (sils) if it (the discharge) does not stop until after the prayer time and his prayer is affected by it, or is it sufficient for him to sprinkle water on his garment and disregard what comes out afterwards?

If the pre-seminal fluid (madhy) does not stop for a sufficient time to attain purity and pray, then your ruling is that of one afflicted with perpetual discharge (sahib al-salas). So, perform ablution (wudu') after the time for prayer begins, and pray with that ablution whatever obligatory and supererogatory prayers you wish until the time for that prayer exits.