The key is it's last minute. Adding a fuselage plug forward of the wing is a not a trivial change - it's a major fuselage re-design. Sure, if you don't mind delaying the project a couple years and tens (or even hundreds) of millions in additional costs.
The location of the wing relative to the fuselage is one of the first things that have to be established when designing an aircraft, not something you can mess with less than a year prior to first flight when you find out the engine just got a lot heavier.
PDR, one ton per engine, there are two (at least). Also, there is already a lot of stuff at the pointy end that can't be readily moved - hence when you start talking thousands of pounds of ballast you can't put it in the most efficient location.

Ah. It seems the weight growth in the anecdote is accelerating faster than it did in the engines. So was the two ton ballast requirement per engine as well? 1 ton of weight growth sounds like rather a lot in a 2-1/2 ton engine...

Yes, those pesky baggage holds can be so difficult to put stuff in, can't they. The last aircraft I was involved with where this order of magnitude of CG error needed correcting the favoured proposal was ti increment the material thickness in the skins and stringers of the forward fuselage, which would have* solved the problem quite easily. It's not rocket surgery.

* I say "would have" because the project was cancelled for other reasons.

Blu-y,
Tail mounted engines can cost a lot in design. Start with the simple fact that, because there are no podded engines to hold down the wings, the wing structure must be heavier to resist the moments generated by lift. Just for starters that is costly. It goes on - do some homework and you'll get the idea. Yes, I know, rudder can be smaller due asymmetrics and that is a saving but there is the fuel system etc, etc.

I thought the clue was 'D9nt' but perhaps it was a typo - all too cunning for me ;)

Not only that, but wing-mounted engines are typically used as torsional dampers, also allowing a lighter wing structure. And of course tail-mounted engines are much higher up, requiring more expensive platforms & lifting gear for maintenance/replacement.

Basil, I'd put my money on one of the Bombadiers, likely one of the Global kind, I'd further bet the 7000 and 8000 with the GE Passport engines. As usual, I'd probably lose the bet if horses are any guide.

PDR, go ahead and be the skeptic, but consider these facts:
The MD-90 incorporated new, 1990's technology V2500 engines to replace the 1960s technology JT-8D engines on the MD-80. This should have provided a huge improvement in fuel burn - but it didn't. The MD-90 operating costs were barely better than the MD-80. As a result, nearly 1200 MD-80s were delivered over 17 years, compared to 116 MD-90's over 6 years before it was euthanized .
People that worked on the MD-90 told me the problem was the aircraft was so severely overweight, with most of that due to the heavy engines and the associated nose ballast.

A little research shows the V2500 is about 900 pounds more per engine than the -217, according to Wiki. Add in the pylon flaps, structure improvements and certainly over a ton-plus total at the wrong location.

High compression turbofans are heavy, an inescapable fact. Also, a reason reengining the CRJ series is a non-starter.

To further your point, they also add operational challenges with FOD induction and lateral stability issues due to rudder blanking as evidenced by the Delta mad dog runway excursion at LGA in 2015.

How can wingmounted engines allow for lighter wing structure.
Torsion damping can not possibly be that heavy on a modern wing.
Compared to all the crap that is associated with an engine on a lifting surface.
Heavy engine on wing = more wing and heavy wing.

I think you misunderstand. With no engines on the wing the structure must be torsionally stiff, and that takes material to do (the torsion loads are usually reacted by the skins which must be thicker to take them). But if you have nice lumps of metal on lever-arms you don't NEED to make the wing torsionally stiff - you just give it a high rotary inertia so that the time-constant on reacting to a torsion upset to likely to be so long that the upset will disappear before it moves significantly. Pylon-mounted engines do just that; they act as torsion-mass dampers, so the skins don't need to be as thick.

I'm sorry, but that's not true. I'm also sure it has been detailed here and elsewhere many times before - google something like wing bending moment relief. Essentially if you put all the weight in the fuselage and all the lift in the wings then all the weight is reacted at the wing root in bending. But if you spread weight across the wings the weight pushing down balances the lift pushing up and that part of the lift never has to appear in the bending moments (either summed at the root or reacted progressively across the span) so the required wing bending strength is much smaller. Therefore you can get away with a much lighter structure.

That's the argument for wing-mounted engines, undercarriages, wing fuel tanks, tip tanks, military stores mounted on wing pylons etc etc.

All of this has been known about since the 707.

Actually since the B-47. When Boeing proposed a swept wing for the B-47 they ran into nasty flutter issues until they figured out how to use the podded engines as mass dampers.

That's the one! (I'd forgotten about the application on the earlier bombers)

The early B747-200s had ballasted nose cowls for the outboard engines for flutter damping we were told.
Another fringe benefit of the engine struts on #1 and #4 was that the inboard edge of the strut was made vertical about 3 inches high and brought aft over the leading edge as a cheap fence, making a virtue out of necessity.