Thank you for enabling the write access. It's much better when debugging something to be able to modify the files
I spent an hour adding traces in the jseblod plugin to figure out where it was messing up and why and how I could fix it without removing functionnalities from it.
Finally, on line 197 of the plugin file plugins/system/cckjseblod.php I found that:
$excluded = '( "mod_mainmenu", "mod_login", "mod_whosonline", "mod_breadcrumbs", "mod_cckjseblod_login", "mod_cckjseblod_siteforms", "mod_cckjseblod_search", "mod_cckjseblod_list", "mod_cckjseblod_ecommerce_cart" )';
to which I added Hikashop's two modules mod_hikashop and mod_hikashop_cart to have this:
$excluded = '( "mod_hikashop", "mod_hikashop_cart", "mod_mainmenu", "mod_login", "mod_whosonline", "mod_breadcrumbs", "mod_cckjseblod_login", "mod_cckjseblod_siteforms", "mod_cckjseblod_search", "mod_cckjseblod_list", "mod_cckjseblod_ecommerce_cart" )';
It seems to be working now.