A larger cap after the rectifier would tend towards a slightly higher HT and less hum . Single ended amps like this dont benefit from the cancelation of HT hum and noise in the transformer that push pull amps do . PSRR or power supply rejection ratio might be 20 db or more worse with single ended .
Fender model 5E1 uses a choke after the first filter , looses it an insignifigant enough 15 volts on the ht but will make it a fair bit quieter if done right .Thats one possible option, Another is adding maybe 5W 150-220 ohm resistor and an extra smoothing cap before B+1 point , you'll loose a small amount of Ht voltage some of which you can recoup by making the first filter cap larger , maybe a 220 uf or more but be sure the voltage rating is respected with a margin to spare . You'll take back hum a noticable bit from what it is now but you will still hear it clearly with your ear from the speaker at minmum volume on the amp . You can add further RC smoothing elements to lower noise more and take a hit on your HT voltage . Ive found for studio usage where your miking up a speaker or DI' ing a small amp like this your less concerned about maximum output wattage or volume , the trade off between power/noise in that situation is a no brainer.
I'm looking at the DC circuit voltages you listed and to be honest all is fairly good , there an allowable margin on everything . The 6V6 screen grid does seem to be pulling a touch more current than expected , you could swap it out with another valve just to double check.
Single ended amps do distort differently to your usual push pull tube amps , clipping is asymetrical.
But if the thing truely breaks loose when overdriven and starts ringing it could be on the verge of osscilation . Its often down to layout , a stray capacitance ( or proximity of wiring) between two different paths in the circuit causes feedback of an unwanted kind often accompanied by buzzes/honks/hums even in the absence of signal .
Be especially carefull of the path your output transformer secondary /feedback resistor/ grid and associated wiring takes back to earlier stages of the amp .A matter of millimeters in proximity to the wrong wire can have a huge effect on how the amp handles under overload especially
When in doubt refer back to the chopsticking methodology by PRR ,