The breadboard setup resulted into the same issue.
I found this post - Bootloader for 8MHz ATMEGA328 - Microcontrollers - Arduino Forum
and this port - Arduino with 8MHz crystal - #7 by JChristensen - Microcontrollers - Arduino Forum
There is optiboot_atmega328_pro_8MHz.hex which user claims is compiled with 8MHz setting.
Believe or not, but once flashed into the Pro Mini, I am able to upload the sketch into it.
This is the boards entry for the mentioned hex file I used:
pro328.name=Arduino Pro or Pro Mini (3.3V, 8 MHz) w/ ATmega328
pro328.upload.tool=arduino:avrdude
pro328.upload.protocol=arduino
pro328.upload.maximum_size=32256
pro328.upload.speed=57600
pro328.bootloader.tool=arduino:avrdude
pro328.bootloader.low_fuses=0xFF
pro328.bootloader.high_fuses=0xDE
pro328.bootloader.extended_fuses=0x05
#pro328.bootloader.path=optiboot
pro328.bootloader.file=optiboot/optiboot_atmega328_pro_8MHz.hex
#pro328.bootloader.path=atmega
#pro328.bootloader.file=optiboot/ATmegaBOOT_168_atmega328_pro_8MHz.hex
pro328.bootloader.unlock_bits=0x3F
pro328.bootloader.lock_bits=0x0F
pro328.build.mcu=atmega328p
pro328.build.f_cpu=8000000L
pro328.build.core=arduino
pro328.build.board=AVR_UNO
pro328.build.variant=standard
This is the difference between "original" optiboot hex file and the one I downloaded from the post above:
diff optiboot_atmega328_pro_8MHz.hex optiboot_atmega328.hex
4c4
< :107E300028E13EEF91E0309385002093840096BBCB
---
> :107E300020E33CEF91E0309385002093840096BBD3