Carrying out a training flight and filling in the associated paperwork (logbook and application form) is something that you should be able to carry out, but the supervision question is the big question mark. I know that various ATOs have differing approaches to this, perhaps it's best to ask the CFI at the facility where you work from. Personally, I would not have a problem with a restricted FI carrying out such a training flight. The restriction on your FI rating is mostly aimed at restricting the risks surrounding first solos and you establishing a basis of instructing experience before training for the CPL and such. Because of this, a training flight with a licence holder should be well within your capabilities and not something that should be restricted by your limited priviliges. But that's just my two cents of course.
You muddied the water there when you mentioned 'could FCL.945 their...' as that normally relates to extending the validity period of the rating by filling in the boxes on the licence and signing this. For that you need to be a FE or have the FCL.945 privilige on your FI rating. But I realise that you're aware of that. Just thought it worth mentioning... to 'un-muddy' the waters again, if that makes sense...