sunds like excessive play on big end rod bearing that may be causing engine seizing at high temperature. If tha's the case and continue riding it you´ll mess the cylinder up. by the way the 03 kx 250 is one fine ride. Luckily rebuilding a smoker isn't as expensive as a high end 450 thumper if the cylinder isn't gone.
it won't fit on top of the 05 cylinder cause the timing and water jackets got a different geometry plus the intake port might be different bein designed for FI. I know this because I tried a 08 cylinder on my 07 and found all that. I know bore's stroke's different too.