UPDATE: Here is what I have done for now:

In separate sketch, EEPROM is filled with binary code. Bootloader (edited optiboot v8):

  // Set up watchdog to trigger after desired timeout
  watchdogConfig(WDTPERIOD);
#if BIGBOOT

  if ((eeprom_read(0x000) == 0x0C) && (eeprom_read(0x001) == 0x94))
  {
    //while (EECR & (1 << EEPE)); //wait if previous data is still being written
    uint8_t i, j;

    for (i = 0; i < 8; ++i) // 8 pages total
    {
      uint8_t *code;
      code = buff.bptr;
      address.word = (i * 128);

      for (j = 0; j < 128; ++j)  // 128 words at a time
      {     
        if (j % 64 == 0)     
          LED_PORT ^= _BV(LED);

        *code++ = eeprom_read(address.word + j);
      }

#ifdef VIRTUAL_BOOT_PARTITION
      virtualBootPartition(buff, address);
#endif 

      writebuffer(0x46, buff, address, 128);
    }

    while(1); // wait for WDT
  }
#endif


#if (LED_START_FLASHES > 0) || LED_DATA_FLASH || LED_START_ON
  /* Set LED pin as output */
  LED_DDR |= _BV(LED);
#endif

while my function looks like this:

#if BIGBOOT 
static uint8_t eeprom_read(uint16_t addr)
{
  EEAR = addr; //read from that address
  EECR |= (1 << EERE); //enable reading

  return EEDR;
}
#endif

I use make atmega328 BIGBOOT=1 to generate hex file. It does not work + UART uploading also fails. If I set BIGBOOT to 0 and generate, UART uploading works fine.

P.S. virtualBootPartition is function which is called in STK_PROG_PAGE case. In order to not repeat the same piece of code, I collected that part into the function.

#ifdef VIRTUAL_BOOT_PARTITION
/*
 *              How the Virtual Boot Partition works:
 * At the beginning of a normal AVR program are a set of vectors that
 * implement the interrupt mechanism.  Each vector is usually a single
 * instruction that dispatches to the appropriate ISR.
 * The instruction is normally an rjmp (on AVRs with 8k or less of flash)
 * or jmp instruction, and the 0th vector is executed on reset and jumps
 * to the start of the user program:
 * vectors: jmp startup
 *          jmp ISR1
 *          jmp ISR2
 *             :      ;; etc
 *          jmp lastvector
 * To implement the "Virtual Boot Partition", Optiboot detects when the
 * flash page containing the vectors is being programmed, and replaces the
 * startup vector with a jump to te beginning of Optiboot.  Then it saves
 * the applications's startup vector in another (must be unused by the
 * application), and finally programs the page with the changed vectors.
 * Thereafter, on reset, the vector will dispatch to the beginning of
 * Optiboot.  When Optiboot decides that it will run the user application,
 * it fetches the saved start address from the unused vector, and jumps
 * there.
 * The logic is dependent on size of flash, and whether the reset vector is
 * on the same flash page as the saved start address.
 */

#if FLASHEND > 8192
/*
 * AVR with 4-byte ISR Vectors and "jmp"
 * WARNING: this works only up to 128KB flash!
 */
#if FLASHEND > (128*1024)
#error "Can't use VIRTUAL_BOOT_PARTITION with more than 128k of Flash"
#endif
  if (address.word == RSTVEC_ADDRESS) {
    // This is the reset vector page. We need to live-patch the
    // code so the bootloader runs first.
    //
    // Save jmp targets (for "Verify")
    rstVect0_sav = buff.bptr[rstVect0];
    rstVect1_sav = buff.bptr[rstVect1];

        // Add "jump to Optiboot" at RESET vector
        // WARNING: this works as long as 'main' is in first section
    buff.bptr[rstVect0] = ((uint16_t)pre_main) & 0xFF;
    buff.bptr[rstVect1] = ((uint16_t)pre_main) >> 8;

#if (SAVVEC_ADDRESS != RSTVEC_ADDRESS)
// the save_vector is not necessarilly on the same flash page as the reset
//  vector.  If it isn't, we've waiting to actually write it.
  } 
  else if (address.word == SAVVEC_ADDRESS) {
      // Save old values for Verify
      saveVect0_sav = buff.bptr[saveVect0 - SAVVEC_ADDRESS];
      saveVect1_sav = buff.bptr[saveVect1 - SAVVEC_ADDRESS];

      // Move RESET jmp target to 'save' vector
      buff.bptr[saveVect0 - SAVVEC_ADDRESS] = rstVect0_sav;
      buff.bptr[saveVect1 - SAVVEC_ADDRESS] = rstVect1_sav;
  }
#else 
        // Save old values for Verify
        saveVect0_sav = buff.bptr[saveVect0];
    saveVect1_sav = buff.bptr[saveVect1];

        // Move RESET jmp target to 'save' vector
        buff.bptr[saveVect0] = rstVect0_sav;
        buff.bptr[saveVect1] = rstVect1_sav;
}
#endif

#else
/*
 * AVR with 2-byte ISR Vectors and rjmp
 */
  if (address.word == rstVect0) {
    // This is the reset vector page. We need to live-patch
    // the code so the bootloader runs first.
    //
    // Move RESET vector to 'save' vector
      // Save jmp targets (for "Verify")
    rstVect0_sav = buff.bptr[rstVect0];
    rstVect1_sav = buff.bptr[rstVect1];
    addr16_t vect;
    vect.word = ((uint16_t)pre_main-1);
    // Instruction is a relative jump (rjmp), so recalculate.
    // an RJMP instruction is 0b1100xxxx xxxxxxxx, so we should be able to
    // do math on the offsets without masking it off first.
    // Note that rjmp is relative to the already incremented PC, so the
    //  offset is one less than you might expect.
    buff.bptr[0] = vect.bytes[0]; // rjmp to start of bootloader
    buff.bptr[1] = vect.bytes[1] | 0xC0;  // make an "rjmp"
#if (SAVVEC_ADDRESS != RSTVEC_ADDRESS)
  } 
  else if (address.word == SAVVEC_ADDRESS) {
    addr16_t vect;
    vect.bytes[0] = rstVect0_sav;
    vect.bytes[1] = rstVect1_sav;
    // Save old values for Verify
    saveVect0_sav = buff.bptr[saveVect0 - SAVVEC_ADDRESS];
    saveVect1_sav = buff.bptr[saveVect1 - SAVVEC_ADDRESS];

    vect.word = (vect.word-save_vect_num); //substract 'save' interrupt position
  // Move RESET jmp target to 'save' vector
  buff.bptr[saveVect0 - SAVVEC_ADDRESS] = vect.bytes[0];
  buff.bptr[saveVect1 - SAVVEC_ADDRESS] = (vect.bytes[1] & 0x0F)| 0xC0;  // make an "rjmp"
  }
#else

  // Save old values for Verify
  saveVect0_sav = buff.bptr[saveVect0];
  saveVect1_sav = buff.bptr[saveVect1];

  vect.bytes[0] = rstVect0_sav;
  vect.bytes[1] = rstVect1_sav;
  vect.word = (vect.word-save_vect_num); //substract 'save' interrupt position
  // Move RESET jmp target to 'save' vector
  buff.bptr[saveVect0] = vect.bytes[0];
  buff.bptr[saveVect1] = (vect.bytes[1] & 0x0F)| 0xC0;  // make an "rjmp"
  // Add rjmp to bootloader at RESET vector
  vect.word = ((uint16_t)pre_main-1); // (main) is always <= 0x0FFF; no masking needed.
  buff.bptr[0] = vect.bytes[0]; // rjmp 0x1c00 instruction
}
  
#endif
#endif // FLASHEND
#endif // VBP