Ouuu a trade change? That's a WHOLE different pickle. Once you are enrolled in the Artillery as an Artillery soldier (even unqualified), the process for transferring to a different unit AND different trade becomes much more complicated. Instead of a simple administrative transfer from one unit's strength to another, you have to go through a VOT process (voluntary occupational transfer). This involves more paperwork, interviews with a Personnel Selection Officer, and cover letters by your CO. This is all in addition to the process for transferring from one unit to another.
I think the best way for this to work is to get both units involved. The way I see it working best is for the Armoured unit to officially hire you, and then "attach post" you to the Artillery unit for the sake of initial admin, kitting out and basic training. This is 100% doable, and isn't actually that much paperwork, but it does require those involved to show a little bit of initiative, and it would require that the two units actually talk to and work with each other. Unfortunately, my experience with the Army reserves does not give me much confidence that this will be easy for them.