General consensus seems to be that the lack of bandwidth - particularly at high frequencies - of the LM308 using a compensation cap in the RAT is what produces the characteristic RAT tone. I've not tried a 741, but have tried an OP07 which sounded similar but not identical. So if you want a different sound than RAT sound, a 741 will probably do that. I'm not sure headroom will make much difference since this is hard clipping anyway, but you can always try. Different clippers make a big difference since they change the gain-versus-clipping-threshold relationship and that ends up with a greater mid and upper mid hump for the same amount of distortion with higher Vf clippers.
i have done blind tests on guitarists, with a bunch of opamps, the difference between the LM308 and the OP07 wasn't heard by them at all. most of them thought the TL071 sounded the best but they found it sounding different from the others, and they thought the uA741 was the original LM308.... go figure.
the difference between the tones is best heard with the filter all the way open, so most bright, but its a minor diference, especially at high volumes.
the op07 and the lm308 have a low slew rate, only 0.3v/uS,
the 741 has 0.5v/us and the 071 has 20v/uS.
its this angle that determines the ''softness'' of the chips.
if you want to not make the IC itself clip, you lose a large part of the character. but if you insist, i recommend soft clipping using double the diodes you use for hard clipping. soft clipping with higher headroom before hard clipping prevents the IC from overdriving, and gives a smoother distortion than allowing the IC to clip.
cheers, Iain