Hi. I bought a new 2005 KX250 less than two weeks ago. My bike is very similar to yours, so maybe I can help. Mine drips oil out of that hose also. I had never heard of such a thing before. I am used to digging it out later on a KDX after it is baked hard onto the power valves. Hooray for whoever came up with the hose to help some.
I am not through with the break-in procedure yet. I am currently running what the dealer put in it, which was said to be Kawasaki oil at 32:1 (which I have run for years on the KDX's). After break-in, I will be switching to Bel-Ray H1R at 40:1. Hopefully, over time, it will be cleaner on the power valve parts.
You may want to check your owner's manual (and hopefully) your service manual, to see what the stock plug is. On mine, the cheap BR8ES is not even listed. The BR8EIX is listed as an optional plug. If you do not run the engine hard, a switch to a 7 heat range plug may benefit you. I used to foul plus often on my 1994 KDX200 until I switched to a one step lower numbered heat range plug (hotter). After that, my plugs were a lovely brown color, not black and dry.
The low end plugs (BR8ES) will foul quicker than a BR8EIX plug. In my manual, it lists the BR8ECMVX (physically less tall), which is difficult to find. I know the BR8ECM (non-VX version) is $10.19 at Rocky Mountain, so you may want to check on that.
If the projected tip sticks down further into the cylinder, that may not be a good idea.
IF, IF, IF your jetting is off, then by all means, start buying some $5 jets and get to testing it.
Remember to stick with one oil and gas mixture to have as few variables as possible during testing. Also, 40:1 will allow more fuel into the engine than a 32:1 mixture. A smaller jet would keep it from taking too big of a gulp.
I hope this helps some. I will be jetting mine soon, so wish us both luck.