Jason,
A 500 NE by Thys would be a very nice rifle for sure!
Cutting (shortening) the barrels on doubles has been done on many different rifles over the years, but it is indeed major surgery and I would only consider doing it on a valuable rifle like yours if there was no other alternative.

The fore-end is another story.
If it was my rifle I too would want a splinter fore-end, but I would not modify the original wood.
Better to keep the original beavertail wood and just have a new splinter style wood made from scratch.
That way you are not affecting the originality of the rifle as the beavertail can be put back at any time in the future.

Back to the barrel length.
You say the gun feels a bit barrel heavy and a bit unwieldy.
It may be possible to shift the balance point back a little so that the rifle has a better feel for your hand positions.
You could also find that you may grip the barrels slightly more forward after the splinter fore-end is fitted, compared to the beavertail, and this would slightly help with the barrel heavyness as well.
To shift the balance point back some weight would need to be added to the buttstock.
If the gun is already a bit heavy this may not be suitable but if you can handle a little extra weight it may be an option.
Remember that even though 26.5 inches sounds long for a double, the overall length of the rifle is going to be shorter than a 24 inch barreled boltgun.
So, maybe, just maybe you could make this rifle handle better in your hands just by having a splinter fore-end wood made, and by bringing the balance point back a tad by weighting the buttstock.

If you do decide to cut the barrels however, my advice would be to make CERTAIN that the work being done, is of a standard equal or better than if it was done by the people who originally built the rifle.

Hope this helps and best of luck with whatever you decide to do.
And yes, some photos if possible please!