Walaykum Assalam dear brother.
I am not exactly sure as to what the activity is, please be more clear on that matter. From my understanding they want you to put your troubles on a paper and that God will help with the difficulty or give advice
When they say 'encounter with God', it depends on what type of christian they are. They may be referring to Prophet Isa(pbuh) or Allah(SWT). It depends on who they are referring to here.
If they are referring to Prophet Isa (pbuh), then it may be taken as shirk as you are indirectly referring to Isa as God.
If it is talking about Allah(SWT), then it is up to you, i personally don't recommend it though just to make sure.
I recently had a dilemma where the novel i was writing could be taken as shirk as the history of the fiction's world didnt come from Allah, but since i didnt believe in it myself nor did my fans or readers, i kept writing while keeping the role of that to the absolute minimum and i try to avoid writing another work with a similar situation just to make sure.
Here, the christians are most probably talking about Isa helping you with your troubles, but the easiest way you can do this is to pray to Allah for guidance on the matter. This is a much safer and easier way.
I am new to this forum, and i'm no scholar nor very knowledgable of Islam, but i try my best to help others live their lives to their fullest while also following their obligations.
May Allah guide you.