As someone who's just getting into the process on my '61 Coupe DeVille, let me save you some time. It is FAR more expensive to swap the motor than to rebuild your 390. Here's just a partial list of what you're looking at with an engine swap:
New transmission obviously, figuring out how to fabricate a shift linkage to your column shift, cooling system (fans, shrouds etc.) and a custom new radiator, throttle linkage, alternator a/c and power steering pump placement and brackets, Firewall and cross member clearance, adapting the rear cross member to whatever transmission, new custom drive shaft, adapting u joints from modern trans to old style rear end, new fuel pump and line (larger) from tank etc. etc Motor mounts can be handled with "adapters", but I'm wary of using an adapter on anything that crucial to the safety and overall integrity of the drivetrain.
Likely some of the above will may be non issues but there's an even longer list that I haven't thought of. My shell shocked and battle weary perspective: If you could get out for $5k on a quality motor re-build and say add another $2k to freshen your tranny, add some bolt ons (carb, intake, HEI) you'll have all the HP and lumpy idle you need for a cruiser and spend half what paying someone else to figure out all the above problems (and more) would cost.
Good luck - it's a long raod, but like you - this is my dream car!
Kenny in DFW