The simplest and cheapest is an appropriately long string of series 1N4007 or (UR4007 / UF4007 for high frequencies).
Add a high value resistor that's rated for at least 1000V and appropriate power across each diode, to balance out the voltage, so no single diode gets overvolts and breaks down.
(eg. 1M Ohm, 1W).
It's a common construction technique for both DIY and commercial rectifiers - though some omit the equalising resistors, which to me is asking for trouble..
Ripple voltage is down to transformer impedance, smoothing capacitors and load current.
The diode type has little or no effect on it - unless you are using antique metal oxide or selenium etc. types, which are far worse than silicon diodes!
Note that 1N4000 series are not fast recovery so only suitable for 50/60 Hz and not much above, regardless of voltage.
You must use the UF or UR versions for high frequency.
Your output capacitor is very small! That is much of the ripple problem.
In real life the transformer is very different than what you have in SPICE. It will be hard to make a transformer with that many turns on the output. The transformer has a self resonant frequency that SPICE is not modeling.
In my example I split the output into two windings (or even more) to reduce the resonant frequency. This also allows for lower voltage diodes to be used.
When you make the transformer we can talk about how to do that.
You picked fast diodes which is good for you 80khz.
I do not have a file for Q6. I am surprised that it turns off well with only 2k to turn it off.
Yes, R14 and C4 are my idea of a small sparkgap.
Here's the model sorry I didn't include it:
.MODEL FJL6920 NPN IS=1.047p NF=0.996 ISE=2.878p NE=1.204 BF=23.7 IKF=7.65 VAF=5.37 NR=1.001 ISC=3.631p NC=1.03 BR=3.23 IKR=4.548 VAR=3.88 RB=94.4 IRB=4.397E-07 RBM=0.082 RE=0.015 RC=0.078 XTB=0.73 EG=1.21 XTI=3 CJE=1.38E-08 VJE=0.583 MJE=0.335 CJC=6.18E-10 VJC=0.284 MJC=0.343 XCJC=0.33 FC=0.5 Vceo=800 Icrating=20 mfg=Fairchild
I hate the NE555 because it is used for too many jobe, but..........
Your base current was very strange causing Q6 to run very hot. I am not happy with it now but Q6 is much cooler. I need to do something with R15 but good for now.
Added D3 because there was/is reverse current.
Added C7 to make this a resonant flyback much like in a cold CRT TV.