Refresh of F5 Equipment

I am reaching out to the group to see if I can get some guidance on how to proceed with a complete refresh of our GTM/LTM environment. We currently have 2 DC's with 2 appliances running both GTM and LTM. The DC's are divided in respective groups for LTM but the GTM's are all part of the one group. We are moving the GTM functionality off to standalone devices (2 at each DC) and will replace the LTM's with 2 devices at each site. I am trying to determine which to move first...Since the GTM is currently "on" box I was thinking moving that functionality first to the new appliances but I am afraid this will cause issues adding these devices. Should the new devices be deployed using the same version so the big3d version is consistent then just add the LTM's to the new GTM via the run gtm bigipadd command, will this cause issues with the current setup? I hoping someone can point us in the right direction or method to do this migration...am I am correct in moving the GTM first then tackling the LTM?

Any help or suggestions are greatly appreciated.

Thanks,

Joe