So much for a light budget, this is going to wind up being all custom parts any way I go. Still probaly cheaper than starting from scratch.
You can build a MKV very reasonably. There are still smiths out there that realize a few hours worth of work blueprinting an action and installing a barrel isn't worth $700+. You can find great smiths that will blueprint and do a barrel job for $300. A quality barrel will run you about $350 for non fluted, $450 for fluted. You can then get a accumark stock for about $250, remove the pressure point and skim bed it yourself. Sure it won't be a fancy $4000 build but the targets won't know it.