There are hundreds of valve circuits out there - use one of those, rather than randomly connecting a pile of parts and hoping it might somehow work (it won't).
Valve output transformers are freely available still, even RS Components sell them.
You also don't use a 12AX7 to feed a speaker transformer, it's a preamp valve - you need a power valve, such as an EL84. For your specific application I would suggest using a triode/pentode, such as the ECL82 or ECL86.
Something similar to this (rather crude version):
Hoffman Amplifiers Tube Amp Forum, Old ('60) italian ECL82 Record Player on the bench (FINAL - UPDATE)
el34world.com