Probably have to ‘hold’ the test clip on the PIC while programming is taking place…if only to make sure you’ve got a solid connection.
And the resistor/LEDs may load down the PGC/PGD lines too much to let the programmer function properly as well.
Desolder the resistors and/or add a jumper to those particular lines… I don’t see why it won’t work.
Read the datasheets. Talks all about putting extra loads on PGC/PGD and the effects on ICSP.