Victor,

this looks good to me:
> osipovmi@blnn724x:/var/osipovmi/cpython []
> $ git fetch vstinner
> remote: Counting objects: 65, done.
> remote: Compressing objects: 100% (18/18), done.
> remote: Total 65 (delta 41), reused 43 (delta 37), pack-reused 10
> Unpacking objects: 100% (65/65), done.
> From https://github.com/vstinner/cpython
>  + 6171da5569...559de620d7 hpux_force_ascii -> vstinner/hpux_force_ascii  (forced update)
>  * [new branch]            posix_locale37   -> vstinner/posix_locale37
> osipovmi@blnn724x:/var/osipovmi/cpython []
> $ git reset --hard  vstinner/hpux_force_ascii
> HEAD is now at 559de620d7 bpo-34403: On HP-UX, force ASCII for C locale
> $ gmake -j 8
> ...
> osipovmi@blnn724x:/var/osipovmi/cpython []
> $ LC_ALL=C ./python -m test -j0 -r -uall,-network
> ...
> == Tests result: FAILURE ==
> 
> 357 tests OK.
> 
> 35 tests failed:
>     test_asyncio test_asyncore test_bytes test_c_locale_coercion
>     test_code test_concurrent_futures test_ctypes test_devpoll
>     test_distutils test_embed test_faulthandler test_fileio test_gdb
>     test_httpservers test_importlib test_io test_mmap
>     test_multiprocessing_fork test_multiprocessing_forkserver
>     test_multiprocessing_main_handling test_multiprocessing_spawn
>     test_normalization test_os test_pkg test_posix test_pty test_re
>     test_signal test_socket test_subprocess test_support
>     test_threading test_time test_unicode test_zlib
> 
> 26 tests skipped:
>     test_curses test_dbm_gnu test_epoll test_idle test_kqueue
>     test_lzma test_msilib test_ossaudiodev test_smtpnet
>     test_socketserver test_spwd test_startfile test_tcl test_timeout
>     test_tix test_tk test_ttk_guionly test_ttk_textonly test_turtle
>     test_urllib2net test_urllibnet test_winconsoleio test_winreg
>     test_winsound test_xmlrpc_net test_zipfile64
> osipovmi@blnn724x:/var/osipovmi/cpython []
> $ ./python -m test -j0 -r -uall,-network
> ...
> == Tests result: FAILURE ==
> 
> 357 tests OK.
> 
> 35 tests failed:
>     test_asyncio test_asyncore test_bytes test_c_locale_coercion
>     test_code test_concurrent_futures test_ctypes test_devpoll
>     test_distutils test_embed test_faulthandler test_fileio test_gdb
>     test_httpservers test_importlib test_io test_mmap
>     test_multiprocessing_fork test_multiprocessing_forkserver
>     test_multiprocessing_main_handling test_multiprocessing_spawn
>     test_normalization test_os test_posix test_pty test_re
>     test_readline test_signal test_socket test_subprocess test_support
>     test_threading test_time test_unicode test_zlib
> 
> 26 tests skipped:
>     test_curses test_dbm_gnu test_epoll test_idle test_kqueue
>     test_lzma test_msilib test_ossaudiodev test_smtpnet
>     test_socketserver test_spwd test_startfile test_tcl test_timeout
>     test_tix test_tk test_ttk_guionly test_ttk_textonly test_turtle
>     test_urllib2net test_urllibnet test_winconsoleio test_winreg
>     test_winsound test_xmlrpc_net test_zipfile64
> 
> Total duration: 14 min 23 sec
> Tests result: FAILURE

The test_utf8_mode passes. Some other tests likely fail due to this Roman8 stuff: test_re and friends. I am analyzing the failures step by step and have already a few fixes around. Waiting for other PRs to be merged first.