Given that the head on the used motor is cracked, I would concur with JD’s suggestion above in purchasing a factory oem short block……..especially if you intend to keep the vehicle.
While a used motor may come with a warranty from the seller, they do not cover the cost to install…….so if it is defective too………you will get a replacement…….but the labor to install and uninstall and then install that replacement is not covered by the seller.
And the key to getting this done with minimal further negative impact to you will be the knowledge and experience of your mechanic.
I have been privy to many a stand-off between the seller of a used motor and the mechanic doing the install. Each blaming the other when a used motor does not function properly when installed…….and the customer becomes the ultimate loser in that battle.
Note that this is not an attempt to influence you in any way, but merely to inform you of the possibilities.
Again, good luck.