In these situations it helps if you can manage more frequent but smaller volume gravel-clean-water-changes. This gives your immature bacterial colonies less excess to have to work on. Eventually they will become big healthy colonies and make quick work of the excess ammonia in your tap water. I too recommend Seachem Prime as somehow seeming to do a higher quality job despite the fact that technically the major real thing we can say that makes it more popular with experienced aquarists is the very high concentration it comes in.
Kind of off the subject but lately I've found myself dreaming of a product that goes like this: it would perhaps look a little like one of those water bags the long-distance exercise runners wear. So it would be a plastic bag with straps to hang on your back and it would have a gravel cleaning tube and perhaps a hand-pump starter. Obviously the bag might have to hang low off your waist or something to get some gravity feed. You'd do a little gravel cleaning, walk to the tub or outside and use a different drain hose it would have and then walk back to your tank and do it again if you needed to. The whole thing would have clips to keep the hoses neat and out of your way and you could hang the whole thing in a cabinet or whatever when not using. I use a nice big hose direct-fill system for my big water changes but I would buy a product like this in a heartbeat to help do smaller "spur of the moment" water changes.
Ah, well, that's waterdrop's little morning coffee thought and now it's off to work for me...
~~waterdrop~~