I do like to keep my loader bucket on while using the rear blade to move snow around.
Here's what I suspect happens;
With the front end in float the load on the front wheels is relatively light, as you said.
When the snow is deep/heavy the resistance to pushing increases, the tendency of the tractor to rotate about it's rear axle (wheelie effect) also increases, further lightening the load on the front wheels.
Subjectively, the steering gets "light", the front wheels plow sideways, etc.
This doesn't happen when back dragging, in fact I clear out tight corners by back dragging the bucket tipped nearly vertical - no quite, I don't want it to snag.
So yes, adding weight to the front grille would probably solve the individual annoyance that is caused by doing something in a way that could be done differently, where "differently" is (subjectively) better for several other reasons, having the bucket on for stacking being one.
If you do this I think you should pay some attention to NOT blocking your lights, or air flow, but most importantly lights.
It seems I always have to clear snow when it is dark, or half light.
I use my 4 way flashers and take an amount of care to keep the bucket low enough for the headlights to shine over it.
A plastic mortar tub would probably make a good mold and in my opinion might be worth keeping on as a soft shield to protect tractor paint, grille, etc. Maybe set eye bolts, or whatever you will use to mount it, through the bottom of it before pouring ?
Yeah, I'm old enough for that problem, but if I don't move I'll seize up entirely.
I've been trying to turn around and look over my LEFT shoulder to ease it, which helps, but that isn't easy either.
The BIGGEST problem I have with looking back is having my wallet and check book escape from my rear pocket, but at THIS age it would be much better for my back to not carry wallets and check books in my butt pockets anyway (-: