Here is a step by step load line procedure. I used a 12AX7 again but this time I am shooting for more gain by increasing Ra.

OK, so let's take this 1 step further now and see what the input threshold of this circuit is.
Vcutoff is 15V, Vtube is 155V, this is a difference of -130V. VB+ is 300V which is +145V above our operating point. This means the negative cycle will start to clip a little before the positive cycle. Vout max is 2x the smaller of the 2 numbers, in this case 130x2=260V
Vout max/AV=Vin max or Vthreshold. 260/83=3.1V That is slightly greater than 2x Vbias. The most you can hit a tube with w/o distortion is 2xVbias so Vthreshold is 3V. It'd be pretty hard to clip this tube with just a geetar as an input but if it were duplicated and installed as V2, you could knock it silly. Let's say your guitar is putting out 1 Volt and it's feeding into V1 so you're getting 83V out. V2 is a duplicate and has a 3V threshold before it starts to clip but we're hitting it with 83V, that's over drive central, or you dial the wiper of Rl of V1 back until you get to 3V for clean undistorted signal.
Now let's look at the curve sheet for the 12AU7.

Right off the bat, notice that plate current tops out 10x higher than a 12AX7. It has curves from 0 to -30V vs. 0 to -5V of the 12AX7. Right off the bat you can plan on drawing more current but being able to hit the tube harder w/o it distorting. Cool so let's design a V2 circuit. Let's get a little more B+, 350V sounds good. Now I drew the load line approximately perpendicular. 350V/23mA is 15k ohms. V cutoff = 120V so Vtube=235V, Vbias=-9V, Itube=7.5mA, Rk=1200 For simplicity sake I plotted Vin=2V and Vout=22V therefore AV=11. vtube is right dead center of VB+ and Vcutoff so Vout max = 230V. 230/11=21, again greater than 2x Vbias so call Vthreshold= 18V Your mileage may vary. I've heard the rule of thumb for Vthreshold is to be equal to Vbias. None the less, you can smack a 12AU7 a lot harder than a 12AX7 before distortion so it is a viable candidate for V2 in a clean amp. Another benefit is the lower output impedance. It's not as low as a cathode follower but low enough to drive a tone stack efficiently. Lok at many of the popular guitar amp tone stacks. The average loss is -10dB. This little circuit is making 21dB. Sandwich a -10dB tone stack between 2 of these and you walk away with +32dB. V1 described is about 38dB. This totals +70dB or AV=3100. You got plenty of output swing to drive any PI or single ended bottle. It'd probably be a nice clean amp.