Quite right.

Take and manipulate your images in adobe rgb and if needed convert a copy to srgb for online printing.

As to Photobox the fuji frontier strips out the profile and uses its own profile, srgb is recommended because it is the closest colour space to the fuji one. You can always get the frontier370 profile from the fuji site to use in Photoshop and use that if you are really fussy and want a exact match.

Likewise although the large format printer mentioned does not strip out your profile it does not use it but ignores it but the adobe RGb colour space is the nearest to this printers colour space so the match is fairly good..at the moment none of the online photolabs I know off do profile conversions as a matter of course.