In my sewing group we have a couple of ladies with physical issues. I am one of the younger/flexible ones and often help particularly one person get her machine in/out of the car, and once inside on to her desk spot.
I bought a lightweight machine and rolling case for myself because I'm not all that young and flexible myself, just in comparison.
Did a little looking and your machine is a couple pounds heavier than mine, but still under 20 pounds. My wheeled bag is only about 5 pounds. You said packed the bag was about 35 pounds -- does that include your project too??
I'd suggest putting your other things in another wheeled tote or bag(s) that you can take out separately. Either put the bag on top of your wheeled case once the handle is pulled out, or trundle along with two cases either.