Try 6BC8. It is an un-sexy TV tuner tube. Cutoff voltage is only around -12V, so it won't take the thumpin input voltages that 6386 will swallow. But at idle (high gain, no GR) it has pretty high transconductance (possibly low noise voltage), and pretty high current (so it will have some current left when in GR). Also significant variation in Mu, about 2.5:1, which eases some design problems a few dB compared to a nearly-constant Mu tube like 12AU7.
It isn't "better". But 6386 are expensive, and while the 6ES8 is fine, it is rare (I think it was a last-gasp attempt to keep tubes ahead of transistor encroachment). 6BA6 is an obvious choice, but finding pairs that match over the whole range is tough. With 6CB8, you know both halves were made in the same place, probably on the same jig by the same worker. And 6BC8 is so cheap, you can experiment with parallels. 8 or 16 of them -might- work without a makeup amp, like the 660 does, for way under $100.
The 6BC8's Ip/Gm is about 1.6V at 10mA, and that is a guideline for the maximum input voltage. In single-ended audio GR, the level must be much less than 1.6V. In push-pull, the maximum input can approach 1.6V before distortion won't cancel and distortion gets gross. The noise voltage may be a couple μV, so the total input dynamic range is around 120dB. Subtract the maximum GR to find the output S/N: 90dB-100dB. Good enough to master vinyl, and not a problem for 16-bit work. And since you only need a volt or so peak input at max GR, and many sources can supply several volts on peaks, you don't need step-up in the input transformer.
> 6386 cuts off at a very, very low voltage (-70 volts or so with a 250 volt plate).
6BA6 is a fairly normal late-1930s tube. Since then most tubes worked for higher transconductance at a given current (to raise gain and reduce power supply cost). That's actually all wrong for an audio limiter: we want low to very-low transconductance, and don't care (much) how much current it eats. The 6386 goes the other direction: it is a "lame" tube as a "cheap amplifier": pretty hungry for the gain it gives. That's what makes it good for GR. You need huge grid voltage to change its Gm, and it still has considerable current at large grid bias and low transconductance, so it can make some power even when far down the curve.