Well, one option is "over the top" ... to have a rail that connects to the top of the scope rings and hangs out over the front of the scope and you hook the clpon to the rail upside down. I think Larue has one of those.
But that is not really much different from getting a custom scope base that is 20 inches long. But if you want it to not be floppy, then it needs to have some "sides" so the top rail has structural support out towards the front. Ken Farrell Manufacturing of Warsaw, MO would build you something like that for maybe $300. There are off the shelf solutions that work with some rifle/chassis combinations, but custom is an option. I done several custom rails/scope bases with Ken Farrell.
One thing in your favor is the NF 4-16x is pretty short, 12.6 inches IIRC !!
For an under $10k budget, the PVS-30 option with a good illuminator will get the 400yd or so job done. Thermal clipon option is over $10k if you want 10x or more magnification on the day scope ... If I was going to do thermal clipon for under $10k I would go with SNIPE, with street price of $7k to $8k. I can squeeze 8x out of a SNIPE and hit 12x24 inch steel at 500yds off tripod consistently. Beyond that, the pulsar thermal clipons will give you 5x for $4k-$5k. In a pinch, the Pulsar clipons can be mounted directly to the scope objective bell, though I don't know anyone who recommends that method, including myself and I used to do it with an old ATN PS-22.