Dittos on the "over-pour" idea. Dumb. Very dumb.
Any movement on the old floor puts the new floor at risk. Concrete is super strong in compression and very weak in bending loads, like heaving. It looks like your footings have moved a little too in a century. Hopefully, they are all done moving!
Your current floor looks like moose-poop. Sorry, that's what a buyer would say if you listed your house. Busting out your floor and doing it right is a labor of love for a garage lover. And, it increases your property values. Make a day out of it. Its not a huge garage.
1. Buy a case of beer. Too much beer causes injuries and dehydrates workers. Buy a couple cases of water too.
2. Have your significant other run for pizza/hoagies/Chinese/BBQ/Col Sanders/etc.
3. The week before, rent a dumpster capable of concrete transport. Ask the company and see if they have a special dumpster for this purpose. Locally, its $299 here in Phoenix. Figure out how you can get the dumpster as close as possible to the garage.
4. Rent a jackhammer. Take small nibbles, no more than 4" into the concrete edge. Use the point tool on the hammer and make sure they give you sharp ones. If you can sharpen along the way once or twice, it will make the job that much easier.
5. As the hammers break it out, have a guy (you!) haul it to a dumpster to be hauled away.
For $500-$575, you have the whole floor removed. Gone. Vaporized.
If you can still move (or the next week) measure you floor depth and make sure you have 4" minimum for the new slab. Export dirt if need be. Consider 6" turn downs a foot out around the footings to ensure any footing movement doesn't affect floor. Plan on running elevated 3/8" rebar across floor in at least 24" sections with a good rebar loop around the entire footer, about 6" inside the footer. This is a great time to run any power you may want in the middle of the floor.
Find a couple guys who know how to work concrete and hire them for the day on a weekend. Lots of guys do side work. You MUST see their work before ordering mud! Plenty of guys have been burned on this forum hiring one guy who lets the load get hot before its worked. Get two guys minimum and be their laborer. Wet the hell out of the pour site the night before to keep the ground cool and with the cover of the building, you should have a great Fall pour. Consider cutting the expansion joints instead of working them in while wet. This works better with epoxy coatings.
Doing a lot of the labor and set-up yourself, you should be able to get this done for around $2000-$2500 -or less. Hey, the results will transform your garage.
Ray