Major issues I immediately see are:
For good thermal performance, the board probably should be 50% wider and longer. At the very least. If I was making the board, I'd make it 2x the linear size of your design. Things are too close together for a power amp the way you've laid them out.
Electrolytic capacitors should not be anywhere near the vacuum tubes. The tubes get scorching hot - they will gladly burn your fingers if you touch them just a few minutes from power-up. Electrolytics hate heat, more-or-less. The hotter they run, the shorter they last (talking about going above room temperature here).
Ideally, you'd want tubes on the top side of the board, and everything else on the bottom side - perhaps connectors included, but I'm not adamant about them.
Even then, those electrolytics may get warmish from conduction through the tube sockets and PCB. But they should be fine as long as they are 105°C, 8000hours (or more) parts.
All the signal/power traces should be on one side of the board - probably the top side, for ease of access in case any post-production "surgery" is needed. That way they won't be buried under all the passive parts.
The bottom side should be an almost uninterrupted ground plane, perhaps with one or two short "jumper traces" to bridge the traces on the signal side that must cross each other. As it stands, the ground plane is highly segmented and won't do its job properly.
There should be a star ground point at the bottom of the output tube's cathode RC circuit. The remaining ground plane and the rectifier ground should converge on that point.
Otherwise, there may be some feedback from the output stage to the preamp stages. Perhaps even the cathode follower and tone control should be included in the sub-plane that defines the star ground. It won't be literally a star, but close: a "blob" of ground plane separated from the rest of it, with just one connection point.
I'm not sure all the resistors are properly rated for power dissipation. You'd want to:
- go through all the resistors on the schematic and determine their average power dissipation
- multiply those dissipations by a factor of 2.5 or 3
- choose the next higher dissipation rating for each resistor, mark it on the schematic, and choose footprints accordingly.
I'm not saying there are problems in that regard - I did not check, but that's an important step you must do. Otherwise you'll have problems with resistors that will discolor and scorch the PCB at best, and just burn out at worst.
You'll want nice turret test points arranged conveniently for access with an oscilloscope probe. At the very least the input, and all the grids.
A safe pick-off from the output tube's plate is also desirable - see the diagram below. The 10pF input capacitance of the scope probe, along with junction capacitance of the Zener diodes, will provide a reasonable response - should be flat from say 50Hz to 15kHz.
There is a tendency to omit such circuits. It invariably ends up in getting tired during the amp bring-up, and connecting a scope probe to the anode. Then it's a 50-50 chance if things will blow up in your face so to speak. On higher power amplifiers with 450+ VDC plate voltages there's a good chance of serious injury. Never mind that having all the exposed test points at a safe potential relative to ground is always desirable.

simulate this circuit – Schematic created using CircuitLab
There may be other issues - I'll leave them for others to find out (no time at the moment to look further).
Overall, you've done a good job for a (presumably) first project. Addressing the issues above should go a long way towards a circuit that will work on the first try.
Additional props for using version control. Excellent!
Resist the temptation to use old stock carbon composition "Allen Bradley style" resistors. Their value can rise significantly if they run hot. Generally speaking, their value will just go up over time, the temperature just changes how fast it drifts up. They have some excess noise compared to thin film / metal resistors. Modern non-inductive thick film and carbon composition resistors are much better than the old stuff in terms of stability.
Do not use wirewound resistors in places in the circuit where their inductance would degrade the circuit's performance.
The soft-start circuit could be refined by using a relay configured to latch on when a pushbutton is pressed, and then open when the power is removed. That way anytime the power is lost, there's no switch to remember to flip back - the soft start series resistor will be always in series with the cathodes on power-up, and until the "START" button is pressed. A relay rated for 9V DC should be fine in this application. For a 6V DC rated relay, a series resistor is needed - the value should be 1/2 of the coil DC resistance, so that about 3V will be dropped across it.
The use of the UF4001 diode is recommended instead of a much slower 1N4001. The ultrafast version (UF!) is much less noisy in this application.

simulate this circuit
And mind that anode (plate) voltage. It's out there to kill you. Use an isolation safety transformer to power the amp. The isolated side's earth terminal goes to the center of the secondary winding, or to one of the ends of that winding, and is not connected to earth. The latter would undo the whole point of safety isolation.