Charging Inductor

Hello fellow enthusiasts,

    I have built a few coils in my time with good results.  I have a
question regarding charging inductors when used also as a low-pass L
section filter.
    I have a 5KV 300ma transformer as the supply charging my .04 micro F
tank capacitor.  V peek occurs at 4 ms of the line cycle which we all know
is 250 Hz.
    If you want 5 time constants you will end up with 20K of impedance to
limit the charging current to about 250ma.  This means you need 12 Henrys
of inductance.
    In the past I only was concerned with filtering the HF and not with
current limiting my transformer.  Now I find if I use 250 micro H as in the
past the transformer often draws too much current and fails.
    The configuration is as follows.  From the tank side going in first is
the safety gaps, then a .01 micro F cap to ground, then a 250 micro H
inductor and finally the secondary of the transformer one side of which is
    Maybe I am thinking about it too much but it is getting expensive as I
have tired several scenarios.  If anyone has a fresh look I would greatly
appreciate the help.

Thanks !