By letting the polish dry you’re allowing it to form a shell which won’t be contiguous to the shoe and will come off either in small flakes or even huge chunks like an eggshell.
I would disagree with wdimagineer2b’s comment regarding the wire wool because unless you’re extremely careful/lucky you run the risk of scuffing or otherwise damaging the top layer of leather.
I would start by using gentle heat from a hair dryer to soften the existing polish, then wipe it off with a paper towel and finish with a brisk brushing with your “putting on” brush. This should get rid of the unevenness and leave you with a firm base to start again. If it doesn’t all come off then keep repeating it until it does.
To bring up the shine then, use a Sylvet cloth, if available, or a piece of well-washed old t-shirt, Kiwi polish (not Parade Gloss) and a small dish of cold water. Start with just a small dab of polish on the cloth and polish it in in small circles. When you feel the cloth just start to drag, dip it lightly into cold water and carry on polishing. keep alternating small dabs of polish and little dips of water and do this in small areas until you’ve covered the whole shoe and it’s all coming up shiny. At this point you may find that the cloth is bringing up the shine but also leaving smears, this is when you need to find a clean section of cloth and start to polish using just water to get rid of the smears. This could take an hour or more for each shoe but once you’ve finished they’ll look grand. Remember not to overpolish or overwet your cloth and that less is more. It’s the polish that does the work and the water is just acting as a lubricant.
BTW There are lots of short cuts to creating shiny shoes and no shortage of people who’ll tell you “the best way” but in my 46 years of experience nothing beats good old hard work.