> 9600 is near the limit for a 4 MHz oscillator.

Why?

You can easily send a bit each 16 XTAL cycles. At 4MHz that is 250kbps:

        movlw   0               ; start
        nop
        nop
        movwf   PORTB

        movlw   0               ; lsb
        btfsc   tmp,0
        movlw   1
        movwf   PORTB

        movlw   0
        btfsc   tmp,1
        movlw   1
        movwf   PORTB

        movlw   0
        btfsc   tmp,2
        movlw   1
        movwf   PORTB

        etc