I don't know if I can help much, but since I have been working on my K-6-2 350 today I am at least a little warmed up on the subject
I think the fastest stock speeds where either 500 or 550 MHz so you are near the max stock speed. the only thing you will be able to do is up the multiplier to 5.5 (this is the highest multiplier) or raise the FSB.
The standard K-6-2 got the most benifit from a faster FSB but the K-6-III and K-6-2+ (or 3+) could benifit either way due to the integrated L2 cache.
The multiplier should be controled by either jumpers or a small set of switches on the motherboard, the FSB could be controlled the same way or in the BIOS (sometimes both).
If I remember correctly somewhere between 600 and 650 MHz was where most K-6-2+ owners stopped due to memory errors or hard drive failures at bus speeds any higher.
I can't remember what the common temps where for the K-6-2+ processors but 60C sounds a little high to me, you might want to verify that the voltage is set right (I think they ran at 1.6v or it might have been 1.8 not sure).
I hope this was a little help at least

good luck