Sometimes, a simple change to a different mouthpiece makes a world of difference into how a sax plays. Regarding its feel, some of your beginner level saxes tend to feel that way.
I remember back in the early 1970's, how my Yamaha YAS-61 alto pro model played much smoother and refined, felt easier to finger than the school's loaner instruments. I don't remember exactly what school sax model I was playing, but it was a beginner model. (Selmer, Le Blanc, King, Buescher, etc., just don't remember.)
The fun thing about the budget sax is that you are less likely to be worried about it playing or taking it on the road, used outdoors in less than ideal weather or in say a motel room or other venue where it could get nicked.
50 years ago, the Army issued me 2 horns, a pro model for concert and combo work, a beginner for outdoor marches and venues where one didn't want to risk damaging the expensive pro model. I learned to make do with either.
If you are looking for another mouthpiece, last November I purchased a Bari (US manufacturer) tenor sax mouthpiece. It was high quality constructed, came with cap and ligature for only $20 US:
Composite Tenor Saxophone Mouthpiece with 0.073" Tip Opening, Round Chamber, Ligature, and Cap - Polished
www.sweetwater.com
I used it for our community band this past Spring. I love the way it plays. Dimension wise, IMO, it is roughly equivalent to a Yamaha 5C. They also sell them for alto sax and clarinet.
If interested, you may be able to find a Canadian source. It is available on Amazon US, so most likely is available on Amazon.ca or your local music store.