Acronis is only going to work it's magic if you are replacing a drive in the same system. But you've stated you're migrating to a completely new system, and therefore will require reinstallation.
I'm not sure what "expensive" application you're talking about, but these should have the ability to move from one system to another via reinstallation. Maybe you could clarify and we could advise better?
A trick that "might" work is to capture your old system as a virtual machine and run it within your new system, virtually. You can grab the old system with VMWare's vCenter Converter, and then use your old system inside VMWare Player. You'll need a decent amount of RAM for this, and if this "expensive application" is 3D intensive, then this option may not be the best. Also, if the "expensive application" ties with the CPU's s/n, the application will ask to be "activated" upon first launch in the new virtual machine.
Both of these tools are free.