I have taken a doe with a mini-30. That being said I bought it because of its looks. At around 1k you could buy a quality, far more accurate, bolt action with decent optics for the same. If you are set on a NYS compliant semi ,for $300 more Browning makes some lovely rifles (BAR). Have never owned or fired one ... but they are pretty.
I use a compliant AR in 6.8 SPC. I'd imagine you could get one down to around 5 pounds before optics if you try.
I know a few people that use Remington 742's in 30-06. Current variant is the 750 and comes in 4 or 5 popular deer calibers. The 742s aren't terribly accurate but are good enough to get the job done at typical NY deer ranges.
the following test data, which shows that the average Fusion MSR bullet penetrated nearly 15 inches of gelatin and expanded to .54 caliber. Most of a bullet's expansion happens within the first inch or so of penetration which means that the Fusion load effectively sends a .54 caliber ball through the vitals of its intended target.
Gelletin Federal Fusion Rem. bullet fired into 10 percent ballistic gelatin at 100 yards
(bullet expanded and penetrated to 15 inches)