Writing buffer overflow exploits without NUL terminated strings

I have the below assembly code global _start

section .text

_start:
    jmp call
pop:
    pop ecx                     ; ECX = address of hello
    xor eax, eax                ; EAX = 0
    xor al, al                   ; EAX = 4 (int 0x80 sys_write)
    inc al
    inc al
    inc al
    inc al
    xor ebx, ebx
    inc ebx                    //Does not work inside exploit
    xor edx, edx
    mov dl, hellolen            ; EDX = length of hello string
    int 0x80

    ; Terminate program
    xor eax, eax
    inc eax                    //Does not work inside exploit
    xor ebx, ebx                ; EBX = return value of 0
    int 0x80
call:
    call pop
    hello: db "Hello World!Ho are you!!!!!"
hellolen equ $-hello

The above code works properly and gives the proper output when run independently.

But when I take objdump of the same and if I try to run through buffer overflow I get the following issues.

Here inc al increments al value properly but inc eax or inc ebx

Could be because in the objdump it shows inc al --> fe c0 inc ebx --> 43 //some one byte number

I also tried the following methods to update eax and ebx

xor ebx, ebx
xor bl, bl
inc bl
movsx ebx, bl
;inc ebx

But here movsx opcode is 0x0f and it does not work as I encounter null terminated string(\x0x\x0f ).