This is a case where some $$ on engineering could save you a lot of work/money.
The anchor loads actually aren't that bad on one of those jib cranes (I have had dozens of installs done) Almost all of them require the same 4x4x4 foundation from the manufacturer. Our facility has a 10" slab and we never needed to cut it to put in a foundation for up to 2T 14' reach, or a 500# 24' reach.
Epoxy set anchors - then nuts on under side, set jib onto nuts and then you can do leveling so it doesn't have a drift. Once you have it set - pack the base with a non-shrink grout. Also by nutting top and bottom you don't impart any of your clamp load to base of the jib into the anchor epoxy and there is no risk of over torquing.
Unless you are a monolithic pour and the base will be over the thick edge you will probably need to do something to your floor but it may not be as much as a 4x4x4 cube.
It might even be possible to do the anchoring to your slab and then encase the base in a block of concrete above grade.
Digging out 2.4yds of dirt from under the floor isn't a small task but if you have a strong back or slave labor (read kids) and a empty checkbook the money for cutting and concrete may well still be ahead of costs of an engineer.
If however you have a buddy that is an engineer of this sort and this is at your residence and there is no paper trail he may be able to do some quick math (and it is quick) to tell you what you need to do or come up with a plan to backyard engineer this to the slab, footing, walls.
I have a Jib in my garage but in my case it attaches to floor and the top plate of wall which changes the anchor load case a whole bunch.
BTW - that Jib and Hoist would cost about $7k if it was all new.
A car lift anchor requirements are wayyy different than those on the anchors in a Jib crane, don't compare the two.