[MrFixr55]

I'm very surprised that you got 21 Volts with the tubes in.  Check wiring.  I'm glad that the tubes tested good.  With 21V across 5 tubes, that's 4V per tube.  The filaments should have been glowing very brightly at that voltage until they burned out rather rapidly.

For those following along especially if new to the hobby, I calculated 150 Ohms based on the Ohm's Law Formula R= E/I, (where R = Resistance, E = Voltage and I = Current).  Based on the fact that each tube in the string is rated 0.050 Amps,  the current across a series string is the same for each resistance in the string, and a total voltage of 7.5V across the tubes (Three 1.5V 5ubes = 4.5V; one 3V tube + the 4.5V from the 3 tubes = 7.5V, then 7.5V / 0.050A = 150 Ohms. A nice little chart for the formulae for Ohm's Law is reproduced below:
   

I think that there is a wiring or socket issue.  If you individually measure the resistance between pins 1 and 7 of each tube, It should not total 271 Ohms.  In fact, it should be a lot lower than 150 Ohms as most filaments have a much lower resistance when cold.

Use a Zener diode above 7.5V.  Not much above but above.  9-9.5V tops.  If you can get an 8.5V diode, that should be great.  It is there for protection, not regulation.  Correct resistor and capacitor values should give you the regulation that you need.

I would still try the 150 ohm resistor substituted for the tubes.  This way, you can measure and troubleshoot without totaling out one or more of these tubes.  If you get 21V with the tubes in place but 7.5 V (or so) with the resistor in place, then check the sockets and wiring.  Something is wrong.

Hope this helps! Don't give up!