It's been about 10 years since I last played with filters, but here's what I remember:
+ Capacitors (C) look like short circuits to high frequencies, and like open circuits to low freq's.
+ Inductors (L) are the opposite, short circuits to low freqs, open circuits to high freqs.
+ Your tank circuit (LC), a cap and ind in parallel, is a band-pass filter, similar to a radio tuner. It will pass voltage and block current over a narrow range. When you try to block current drawn by a current source, you get super-high voltages, which is just what you experienced.
+ Put the cap and ind in series (LC) and you get a band-block filter, it will short current and give you zero voltage over a small range of frequencies. Voltage will approach zero over the bandwidth of the filter, current will be about equal to that drawn by your current source.
+ Caps and resistors (RC) or Inds and res (RL) will give you high pass or low pass depending on the configuration. Resistors burn real power, though, so you probably do not want to add your own resistance to the circuit, you'd want to use only caps and inds in your design. In a low-pass configuration, voltage will approach zero above the break frequency ("knee"

of the filter , current will be about equal to that drawn by your current source.
This said, and given the assumption that you are trying to short (band-block) frequencies from 180-720 Hz, or from 420-720Hz, or trying to low-pass (high-block) all freqs below 180Hz or 420Hz, I'd recommend trying the following configurations:
1. Capacitor in parallel with harmonic load. Shorts high frequencies (the cap supplies the high freq current required by the load). Actually an RC circuit, where you provide the cap as part of your filter, and the harmonic load is the resistance.
2. Capacitor in parallel with the harmonic load, with an inductor in series between the hot source and the cap/load. The inductor would help prevent any harmonic currents from making their way back to the panelboard. This is an LC or an LRC circuit.
You will have high currents with either configuration. You cannot avoid this, as the load looks like a current source. The RMS value of the harmonic current will be roughly of the same magnitude as the rated current of your load. The instantaneous harmonic current could be much higher, though; I don't know for sure, but it would not surprise me if the instantaneous harmonic current was 10x or 100x the RMS current. FUSE YOUR CAPACITOR TO KEEP IT FROM BLOWING UP.
Other problems with capacitors on AC systems in general are that they can raise voltages due to transient switching, and they can resonate with the inductance in the rest of the power system causing steady-state overvoltages. Carful with this, you don't want your 120-volt PC to get hit with 200 or 400 volts. You may need to detune your filter to avoid such problems and make it appear resistive or slightly inductive at 60Hz, careful selection of the component sizes used in design #2 above should help with that.
The whole problem with switchmode power supplies (by far the largest source of harmonics) is that they draw all their current over a very short period, maybe only 10% duty cycle. "Nice" loads like motors and incandescent lights use 100% of the cycle, and have a nice sinusoidal current waveform. PC's and other harmonic loads have "spikey" current waveforms. In a quick burst or pulse, they draw all of their energy, and the rest of the cycle they are essentially shut off. When they are turned on, the high current draw causes a voltage drop, which looks like a "bite" out of the voltage waveform. Your filter should provide that pulse current, rather than forcing an upstream transformer to do it.
Hope this helps.