I ground 2400sqft with a 20" floor buffer and a rented diamabrush diamond wheel. You need the right one. There are 2, a mastic remover with fewer diamond encrusted blades, and a concrete prep version with like 20 blades. You can easily remove 1/8", but won't be super fast. You can smooth and sorta level. You could try a hand grinder, but I doubt you'd be happy with the result. My local home center rents that blade for like $50/half day and if you rent in the afternoon, you can return it in the morning for 1/2 day. You should be able to fix that door opening in 1/2 day and it would be great.
FWIW, I rented that grinding thing for several days, at the end of which, I went out and bought one. I want to do my garage and my shop. They are like $700. Pretty sure I had a coupon for Zoro. I own the buffer. I was able to do all the initial grind on my floor (ground floor of my house to be) but hired a floor finisher to do the final polishing. For my shop, I think I will grind, then use coarse scotch brute pads to polish to whatever I can get, then densify and polish/burnish and be done. Won't be glossy, but straight from the grinder, the floor looks pretty great.
More:
We had a new floor poured and the contract said full polish and the contractor agreed. Day off, they said "no polish", hadn't priced that, couldn't do it. We fed them lunch. They used my tools, lasers for heights, wheel barrows, and they left me with this:

I had asked them about power trowels and they said "oh yes yes". But there were no power trowels used. I think they got tired and got off the floor too quickly. I was pretty upset about all of it. They were immigrants and not what I would call cheap.
A couple hours (like 2) with the grinder, I had this:

Had to see but the swirl and trowel marks were gone. You can see a little roughness around the drain pipes.

The concrete polisher guys were not super expensive. This is obviously the opening for where the stairs will be to the second floor. I lined the exterior walls with rigid foam to make a thermal break, since these are heated floors. For anyone interested, this wall is the bank side of the bank barn. We excavated it, parged it, waterproofed then, then spray foamed 2-3" and reburied it (along with a French Drain). So this exposed stone wall is acceptable for the interior. This photo was taken several years ago, there is no moisture ingress, and the floor has a few minor hairline cracks (that happened almost immediately) but no big ones anywhere.
I would not hesitate to rent a buffer and a grinding wheel and go to town on a garage. I started this thanks to inspiration from Garage Journal and I bought densifier from one of the vendors here. My garage floor is a broken uneven mess and I'm looking forward to the end of this project when I may rip it out and repour a new floor like this one. May even heat it like this one, because that was also easy.