> So I got tired of constantly popping the F84 out of its socket and into the
>  programmer, and decided to make an ICSP header on my test board, and rig a
>  cable to the programmer (the ITU PIC-1).
>
>  The problem I've run into is the oscillator. While the programmer is doing
>  its thing, it is supplying +5 to the F84, and the rest of the circuit,
>  which makes the oscillator do its thing, and thus the programming fails.
>
>  If I pop the oscillator out before programming, everything works fine.

Am I very wrong if I don't see the problem?
I don't know how your programmer works, but mine (one of these self
constructed & programmed prototype programmers) takes absolute control of the
MCLR voltage. In programming mode the voltage can be 0V or 13V, the same in
one of my big projects with ICSP abilities. I do this by setting a jumper from
running to programming position.
The newest programming spec for the PIC16F84 says: "The OSC must not have 72
osc clocks while the device MCLR is between VIL and VIHH." At my programming
method this never happens.
I think you use this little "typical in-system serial programming connection"
shown in the PIC databook which I found to be a bit too simple...
I can also imagine an ICSP connector on which you normally plug a jumper to
connect the MCLR pin to the normal reset circuit. While programming you pull
this jumper and connect the programming cable.

Hope it helped
Florian

ps: never programmed a PIC16F(!)84, only PIC16C84s because I haven't run out
of them yet.